Question

How do you find the inverse of `f(x) = (x + 2)^2` and is it a function?

Answer 1

`f^-1(x)=sqrtx-2`

The inverse is a function.

Explanation:

Find the inverse by switching `x` and `y` and solving for `y`.

`y = (x+2)^2`

Switch `x` and `y`.

`x = (y+2)^2`

Solve for `y`. Begin by taking the square root of both sides. Note that taking the square root of something squared is that number (`sqrt(x^2) = x`).

`sqrtx = sqrt((y+2)^2)`

`sqrtx = y+2`

`sqrtx-2 = y`

`y = sqrtx-2`

The inverse of `y=(x+2)^2` is:

`f^-1(x)=sqrtx-2`

The graph of the inverse takes the form of what follows:

graph{sqrt(x)-2 [-10, 10, -5, 5]}

The inverse is a function.