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







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  • $begingroup$
    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


0



$begingroup$


(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
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$begingroup$

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









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    Answer



    thanks for help coffeemath






    share|cite|improve this answer









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      2 Answers
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      2 Answers
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      $begingroup$

      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

          2,8351415




          2,8351415























              1












              $begingroup$

              Answer



              thanks for help coffeemath






              share|cite|improve this answer









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                1












                $begingroup$

                Answer



                thanks for help coffeemath






                share|cite|improve this answer









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                  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






























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