Find the largest possible domain and the largest possible range of $F(x)$












2












$begingroup$


(a) Let $F(x)=1+cos2x$ .
Find the largest possible domain and the largest possible range of $F(x)$.



(b) $G(x)=x^2+2x-2, ;x in [0, infty)$. Find the inverse function $G^{-1}(x)$ and state its domain.



Here is the picture of the question:
enter image description here






functions







share|cite|improve this question











$endgroup$












  • $begingroup$
    Are these test questions? [4 marks, 6 marks made me think they are]
    $endgroup$
    – coffeemath
    Dec 8 '18 at 11:25










  • $begingroup$
    past exams question, given by teachers is it not allowed to post?
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:30










  • $begingroup$
    if not allowed i will delete it
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:30






  • 1




    $begingroup$
    past exam OK. You're claiming past if posting it. I just wanted to make sure not a present take-home.
    $endgroup$
    – coffeemath
    Dec 8 '18 at 11:32






  • 1




    $begingroup$
    yeah don't worry it is past ones
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:34
















2












$begingroup$


(a) Let $F(x)=1+cos2x$ .
Find the largest possible domain and the largest possible range of $F(x)$.



(b) $G(x)=x^2+2x-2, ;x in [0, infty)$. Find the inverse function $G^{-1}(x)$ and state its domain.



Here is the picture of the question:
enter image description here






functions







share|cite|improve this question











$endgroup$












  • $begingroup$
    Are these test questions? [4 marks, 6 marks made me think they are]
    $endgroup$
    – coffeemath
    Dec 8 '18 at 11:25










  • $begingroup$
    past exams question, given by teachers is it not allowed to post?
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:30










  • $begingroup$
    if not allowed i will delete it
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:30






  • 1




    $begingroup$
    past exam OK. You're claiming past if posting it. I just wanted to make sure not a present take-home.
    $endgroup$
    – coffeemath
    Dec 8 '18 at 11:32






  • 1




    $begingroup$
    yeah don't worry it is past ones
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:34














2












2








2


1



$begingroup$


(a) Let $F(x)=1+cos2x$ .
Find the largest possible domain and the largest possible range of $F(x)$.



(b) $G(x)=x^2+2x-2, ;x in [0, infty)$. Find the inverse function $G^{-1}(x)$ and state its domain.



Here is the picture of the question:
enter image description here






functions







share|cite|improve this question











$endgroup$




(a) Let $F(x)=1+cos2x$ .
Find the largest possible domain and the largest possible range of $F(x)$.



(b) $G(x)=x^2+2x-2, ;x in [0, infty)$. Find the inverse function $G^{-1}(x)$ and state its domain.



Here is the picture of the question:
enter image description here






functions




functions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 8 '18 at 12:03









amWhy

1




1










asked Dec 8 '18 at 11:22









auxy12auxy12

257




257












  • $begingroup$
    Are these test questions? [4 marks, 6 marks made me think they are]
    $endgroup$
    – coffeemath
    Dec 8 '18 at 11:25










  • $begingroup$
    past exams question, given by teachers is it not allowed to post?
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:30










  • $begingroup$
    if not allowed i will delete it
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:30






  • 1




    $begingroup$
    past exam OK. You're claiming past if posting it. I just wanted to make sure not a present take-home.
    $endgroup$
    – coffeemath
    Dec 8 '18 at 11:32






  • 1




    $begingroup$
    yeah don't worry it is past ones
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:34


















  • $begingroup$
    Are these test questions? [4 marks, 6 marks made me think they are]
    $endgroup$
    – coffeemath
    Dec 8 '18 at 11:25










  • $begingroup$
    past exams question, given by teachers is it not allowed to post?
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:30










  • $begingroup$
    if not allowed i will delete it
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:30






  • 1




    $begingroup$
    past exam OK. You're claiming past if posting it. I just wanted to make sure not a present take-home.
    $endgroup$
    – coffeemath
    Dec 8 '18 at 11:32






  • 1




    $begingroup$
    yeah don't worry it is past ones
    $endgroup$
    – auxy12
    Dec 8 '18 at 11:34
















$begingroup$
Are these test questions? [4 marks, 6 marks made me think they are]
$endgroup$
– coffeemath
Dec 8 '18 at 11:25




$begingroup$
Are these test questions? [4 marks, 6 marks made me think they are]
$endgroup$
– coffeemath
Dec 8 '18 at 11:25












$begingroup$
past exams question, given by teachers is it not allowed to post?
$endgroup$
– auxy12
Dec 8 '18 at 11:30




$begingroup$
past exams question, given by teachers is it not allowed to post?
$endgroup$
– auxy12
Dec 8 '18 at 11:30












$begingroup$
if not allowed i will delete it
$endgroup$
– auxy12
Dec 8 '18 at 11:30




$begingroup$
if not allowed i will delete it
$endgroup$
– auxy12
Dec 8 '18 at 11:30




1




1




$begingroup$
past exam OK. You're claiming past if posting it. I just wanted to make sure not a present take-home.
$endgroup$
– coffeemath
Dec 8 '18 at 11:32




$begingroup$
past exam OK. You're claiming past if posting it. I just wanted to make sure not a present take-home.
$endgroup$
– coffeemath
Dec 8 '18 at 11:32




1




1




$begingroup$
yeah don't worry it is past ones
$endgroup$
– auxy12
Dec 8 '18 at 11:34




$begingroup$
yeah don't worry it is past ones
$endgroup$
– auxy12
Dec 8 '18 at 11:34










2 Answers
2






active

oldest

votes


















2












$begingroup$

Your first function is defined for any real $x$ so "largest possible domain" is all reals. Then "largest possible range' [if it means range if you use largest domain] can be found by noting the cosine part varies from $-1$ to $1$ and you're adding $1$ to that.



Second function: solve $y=x^2+2x-2$ for $x$ in terms of $y$ using quadratic equation. Whatever is under the radical needs to be zero or more, and remember you still need $x ge 0,$ so that may further restrict $y.$ A sketch will help here.






share|cite|improve this answer









$endgroup$





















    1












    $begingroup$

    Answer



    thanks for help coffeemath






    share|cite|improve this answer









    $endgroup$













      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3030978%2ffind-the-largest-possible-domain-and-the-largest-possible-range-of-fx%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      2












      $begingroup$

      Your first function is defined for any real $x$ so "largest possible domain" is all reals. Then "largest possible range' [if it means range if you use largest domain] can be found by noting the cosine part varies from $-1$ to $1$ and you're adding $1$ to that.



      Second function: solve $y=x^2+2x-2$ for $x$ in terms of $y$ using quadratic equation. Whatever is under the radical needs to be zero or more, and remember you still need $x ge 0,$ so that may further restrict $y.$ A sketch will help here.






      share|cite|improve this answer









      $endgroup$


















        2












        $begingroup$

        Your first function is defined for any real $x$ so "largest possible domain" is all reals. Then "largest possible range' [if it means range if you use largest domain] can be found by noting the cosine part varies from $-1$ to $1$ and you're adding $1$ to that.



        Second function: solve $y=x^2+2x-2$ for $x$ in terms of $y$ using quadratic equation. Whatever is under the radical needs to be zero or more, and remember you still need $x ge 0,$ so that may further restrict $y.$ A sketch will help here.






        share|cite|improve this answer









        $endgroup$
















          2












          2








          2





          $begingroup$

          Your first function is defined for any real $x$ so "largest possible domain" is all reals. Then "largest possible range' [if it means range if you use largest domain] can be found by noting the cosine part varies from $-1$ to $1$ and you're adding $1$ to that.



          Second function: solve $y=x^2+2x-2$ for $x$ in terms of $y$ using quadratic equation. Whatever is under the radical needs to be zero or more, and remember you still need $x ge 0,$ so that may further restrict $y.$ A sketch will help here.






          share|cite|improve this answer









          $endgroup$



          Your first function is defined for any real $x$ so "largest possible domain" is all reals. Then "largest possible range' [if it means range if you use largest domain] can be found by noting the cosine part varies from $-1$ to $1$ and you're adding $1$ to that.



          Second function: solve $y=x^2+2x-2$ for $x$ in terms of $y$ using quadratic equation. Whatever is under the radical needs to be zero or more, and remember you still need $x ge 0,$ so that may further restrict $y.$ A sketch will help here.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Dec 8 '18 at 11:44









          coffeemathcoffeemath

          2,6881413




          2,6881413























              1












              $begingroup$

              Answer



              thanks for help coffeemath






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                Answer



                thanks for help coffeemath






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  Answer



                  thanks for help coffeemath






                  share|cite|improve this answer









                  $endgroup$



                  Answer



                  thanks for help coffeemath







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 8 '18 at 12:11









                  auxy12auxy12

                  257




                  257






























                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3030978%2ffind-the-largest-possible-domain-and-the-largest-possible-range-of-fx%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      -

                      Popular posts from this blog

                      Berounka

                      Image
                      Berounka.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Caractéristiques Longueur 139  km Bassin 8 861  km 2 Bassin collecteur Elbe Débit moyen ? Cours Source Confluence de la Mže et de la Radbuza · Localisation Pilsen · Altitude 305  m · Coordonnées 49° 45′ 13″ N, 13° 23′ 24″ E Confluence Vltava · Localisation Prague · Altitude 187  m · Coordonnées 49° 59′ 43″ N, 14° 24′ 04″ E Géographie Pays traversés   République tchèque modifier   La Berounka est une rivière de la République tchèque. Elle porte le nom de Mže depuis sa source en Allemagne près de la frontière jusqu'à sa confluence avec la Radbuza à Plzeň. Elle continue ensuite sous le nom de Berounka jusqu'à sa confluence avec la Vltava, près de Prague. La rivière est une destination prisée pour les amateurs de canoë, qui appréc...
                      Read more

                      Sphinx de Gizeh

                      Image
                      Pour les articles homonymes, voir Sphinx. Sphinx de Gizeh.mw-parser-output .entete.egypte-antique{background-image:url("//upload.wikimedia.org/wikipedia/commons/c/cc/Picto_infobox_ancient_Egypt.png")} Site d'Égypte antique Le visage du sphinx de Gizeh. Noms en arabe أبو الهول , Abou al-Hôl Localisation Région Basse-Égypte Coordonnées 29° 58′ 31″ nord, 31° 08′ 16″ est Géolocalisation sur la carte : Égypte Sphinx de Gizeh modifier   Le sphinx de Gizeh est la statue thérianthrope qui se dresse devant les grandes pyramides du plateau de Gizeh, en Basse-Égypte. Sculpture monumentale monolithique la plus grande du monde [ 1 ] avec 73,5 mètres de longueur, 14 mètres de largeur et 20,22 mètres de hauteur, elle représente un sphinx couchant. Réalisée vers -2500, elle serait attribuée à Djédefrê, l'un des pharaons de la IV e  dynastie, représentant son père le pharaon Khéops. Sommaire 1 Étymologie 2 Desc...
                      Read more

                      Different font size/position of beamer's navigation symbols template's content depending on regular/plain...

                      Image
                      3 Let's suppose I'd like to divert the navigation symbols template (e.g. in order replace them by the frame numbers, see this bug report ;) I would be facing troubles regarding the font size/position, depending on regular/plain frames, as shown by the following MCE. How could I get rid of these troubles? documentclass{beamer} usetheme{PaloAlto} setbeamertemplate{navigation symbols}{insertframenumber/inserttotalframenumber} begin{document} begin{frame} frametitle{A regular frame} end{frame} begin{frame}[plain] frametitle{A plain frame} end{frame} end{document} beamer header-footer share | improve this question asked Dec 10 '18 a...
                      Read more