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