Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Need this soon please -

Select the correct answer.
What is the inverse of function
f(x)=√x + 7


Need This Soon Please Select The Correct Answer What Is The Inverse Of Function Fxx 7 class=

Sagot :

GʀɪᴍRᴇᴀᴘᴇʀ

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

  • Option A is correct

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Find inverse of given function :

[tex]\qquad❖ \: \sf \:y = \sqrt{x} + 7[/tex]

[tex]\qquad❖ \: \sf \: \sqrt{x} = y - 7[/tex]

[tex]\qquad❖ \: \sf \:x = (y - 7) {}^{2} [/tex]

Next, replace x with f-¹(x) and y with x ~

[tex]\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} [/tex]

we got our inverse function.

Condition : x should be greater or equal to 7

because we will get same value of y for different x if we also include values less than 7.

[tex] \qquad \large \sf {Conclusion} : [/tex]

  • Correct option is A
Kailes

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:

[tex]\longrightarrow\bold{f(x)= \sqrt{7}}[/tex]

To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.

[tex]\bold{Becomes,}[/tex]

Next step we switch sides for x and y variables and then solve for the y variable as shown below,

[tex]\longrightarrow\sf{y= \sqrt{x}+7}[/tex]

[tex]\bold{Then,}[/tex]

[tex]\longrightarrow\sf{x= \sqrt{y}+7}[/tex]

[tex]\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }[/tex] [tex]\bold{sides,}[/tex]

[tex]\longrightarrow\sf{x-7= \sqrt{y}}[/tex]

[tex]\small\bold{Square \: both \: sides }[/tex]

[tex]\sf{(x-7)^2=(\sqrt{y})^2}[/tex]

[tex]\sf{(x-7)^2=y}[/tex]

We now re-write in function notation. Take note however that this is the inverse:

[tex]\bold{Where \: y}[/tex] [tex]\sf{=(x-7)^2 }[/tex]

[tex]\longrightarrow\sf{y= (x-7)^2 }[/tex]

[tex]\huge\mathbb{ \underline{ANSWER:}}[/tex]

[tex]\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }[/tex]

View image Kailes
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.