Finding the Inverse of a Logarithmic Function with a Quadratic Argument

Question

$f(x)=\log_2(x^2-3x-4)$

Find $f^{-1}(x)$

My approach:

$y=\log_2(x^2-3x-4)$

$x=\log_2(y^2-3y-4)$

$2^x=y^2-3y-4$

$2^x+4=y(y-3)$

This is where I am stuck in my attempt on the problem.

Answer 1

$f$ is not injective. Inverse does not exist.