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

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Answer 1 · 2016-07-20T02:35:35

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

The inverse is a function.

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.