Question

Let f(x) = (1-4x) / (4-x)

Find f^-1
Which is actually the inverse

Answer 1

Okay....so the inverse of a function is a function such that \[f(f ^{-1}(x))=1\]

Right?

Answer 2

I thought it would be such that f(f^-1(x)) = x

Im probably wrong...

Answer 3

No you are right. :) It's been a little while since I've done inverses.

Answer 4

Okay, to find the inverse we can solve y=f(x) for x:

y=(1-4x)/(4-x)
(4-x)*y=1-4x
4y-xy+4x-1=0
4y-1-xy+4x=0
4y-1-x(y+4)=0
-x(y+4)=1-4y
-x=(1-4y)/(y+4)
x=(4y-1)/y+4 = f^(-1)(x)



Check my arithmetic and algebra cause I get really sloppy!!

Answer 5

Excellent!