How do you find the inverse of # (x + 2)^2 - 4# and is it a function?

1 Answer
Noah G
Apr 21, 2016

The inverse of a function is found algebraiccally by switching the x and y values.

Explanation:

#y = (x + 2)^2 - 4 -> x = (y + 2)^2 - 4#

#x + 4 = (y + 2)^2#

#+-sqrt(x + 4) = y + 2#

#+-sqrt(x + 4) - 2 = y#

#f^-1(x) = +-sqrt(x + 4) - 2#

This is not a function, because of the #+-# sign. For example, we can substitute x = 12 into the function to find y.

#y = sqrt(12 + 4) - 2#

or

#y = -sqrt(12 + 4) - 2#

#-> y = 2#

or

#-> y = -6#

Since the definition of a function is a relation where each x value has one and only one y value, and that this function contains the points #(12, 2) and (12, -6)#, this is not a function.

Hopefully you understand now!

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