Math Help - Algebraically disproving equal functions

1. Algebraically disproving equal functions

Hey,

Given the function f(x)=3x-4, show algebraically, that f^-1(x) is NOT equal to f(x).

Do I solve for the inverse equation to get y=1/3(x+4) and then sub in values for (x) to get different y-values that do not equal each other? How else could I prove this?

Thanks!

2. Originally Posted by MATHDUDE2
Hey,

Given the function f(x)=3x-4, show algebraically, that f^-1(x) is NOT equal to f(x).

Do I solve for the inverse equation to get y=1/3(x+4) and then sub in values for (x) to get different y-values that do not equal each other? How else could I prove this?

Thanks!
If $f(x) := y = 3x - 4$ then $f^{-1} := x = 3y - 4$

Some rearranging gives

$3y = x + 4$

$y = \frac{1}{3}x + \frac{4}{3}$.

I think it's pretty clear that $f(x) \neq f^{-1}(x)$ for all x.