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)=√(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)=√(x)+7 \\ \\ Becomes: \\ \\ y=√(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=√(x)+7 \\ \\ Becomes: \\ \\ x=√(y)+7 \\ \\ Solve\text{ }for\text{ }y; \\ \\ Subtract\text{ }7\text{ }from\text{ }both\text{ }sides: \\ \\ x-7=√(y) \\ \\ Square\text{ }both\text{ }sides: \\ \\ (x-7)^2=(√(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.