Question

Need this soon please - Select the correct answer.What is the inverse of functionf(x)=√x + 7

Answer 1

GIVEN:

We are given the following function;

$f(x)=\sqrt{x}+7$

Required;

To find the inverse of the function.

Step-by-step solution;

To solve for the inverse of a function f, we begin by re-writing the function as an equation in terms of y. We now have;

$\begin{gathered} f(x)=\sqrt{x}+7 \\ \\ Becomes: \\ \\ y=\sqrt{x}+7 \end{gathered}$

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

$\begin{gathered} y=\sqrt{x}+7 \\ \\ Becomes: \\ \\ x=\sqrt{y}+7 \\ \\ Solve\text{ }for\text{ }y; \\ \\ Subtract\text{ }7\text{ }from\text{ }both\text{ }sides: \\ \\ x-7=\sqrt{y} \\ \\ Square\text{ }both\text{ }sides: \\ \\ (x-7)^2=(\sqrt{y})^2 \\ \\ (x-7)^2=y \end{gathered}$

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

$\begin{gathered} Where\text{ }y=(x-7)^2 \\ \\ f^{-1}(x)=(x-7)^2 \end{gathered}$

Therefore,

ANSWER

$f^{-1}(x)=(x-7)^2\text{ };for\text{ }x\ge7$

The correct answer is option A.