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
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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