# Math Help - Inverse function question

1. ## Inverse function question

Suppose $f(x)$ coincides with its inverse over a suitable interval.

Suppose that $f(x) = \frac{ax+b}{cx+d}$. What conditions on a,b,c,d are necessary and sufficient in order that $f(x)$ coincide with it's inverse function?

Help is greatly appreciated. Thanks.

2. $f^{-1}(x) = {b-dx\over cx-a}$

btw, I think you meant $ax+b\over cx + \color{red}d$.

$f^{-1}(x) = {b-dx\over cy-a}$
btw, I think you meant $ax+b\over cx + \color{red}d$.
Equate $f(x) = f^{-1}(x)$ and clear the denominators. You will arrive at two polynomials in x. Equating their coefficients should give you the required conditions.