Question

Select the correct answerWhat is the inverse of function f?

Answer 1

D

1) Considering that function, we can proceed to find its inverse

`f(x)=\sqrt[]{x}+7`

2) Swap the variables:

`\begin{gathered} y=\sqrt[]{x}+7 \\ x=\sqrt[]{y}+7 \end{gathered}`

3) Let's place the y term on the left and isolate it:

`\begin{gathered} x=\sqrt[]{y}+7 \\ x-7=\sqrt[]{y}+7-7 \\ x-7=\sqrt[]{y} \\ (x-7)^2=(\sqrt[]{y})^2 \\ y=(x-7)^2 \\ f^(-1)(x)=(x-7)^2 \end{gathered}`

Note that x has to be greater or equal to 7

4) Hence, the answer is D