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

##### 1 Answer

Jul 20, 2016

The inverse is a function.

#### Explanation:

Find the inverse by switching

#y = (x+2)^2#

Switch

#x = (y+2)^2#

Solve for

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

#sqrtx = y+2#

#sqrtx-2 = y#

#y = sqrtx-2#

The inverse of

#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.