Posted by **Heather** on Tuesday, January 14, 2014 at 10:48am.

For the function f(x)=(3-4x)^2, find f^-1. Determine whether f^1 is a function.

- Algebra 2 help. -
**Damon**, Tuesday, January 14, 2014 at 11:27am
y = (3-4x)^2

find inverse

x = (3-4y)^2

3 -4y = + or - sqrtx

4 y = 3 + or - sqrt x

y = (3/4) +/- sqrt x

this is not a function because there is more than one value of y for eaxh value of x (vertical line rule)

- Algebra 2 help. -
**Steve**, Tuesday, January 14, 2014 at 11:30am
f^-1 is not a function, since f(x) sends two different elements from the domain to the same element of the range.

f must be 1-to-1 for it to have an inverse. f has two distinct branches:

y = (3-4x)^2

3-4x = ±√y

4x = 3±√y

x = (3±√y)/4

So, there is one branch

f^-1 = (3+√y)/4

and the other (3-√y)/4

where y >= 0

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