Algebra 2 help.
posted by Heather on .
For the function f(x)=(34x)^2, find f^1. Determine whether f^1 is a function.

y = (34x)^2
find inverse
x = (34y)^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) 
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 1to1 for it to have an inverse. f has two distinct branches:
y = (34x)^2
34x = ±√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