The question I'm trying to solve requires me to get the $f^{-1}(x)$ where $f(x)= x^3 + 2x^2 + 4x + \sin (\pi x/2)$ , but I don't know to proceed with such problems with higher degrees of x (and the trigonometric functions don't help much either) . Any methods , prerequisites and ideas for intuitive approaches will be appreciated
According to the question I'm solving , $f:R$ to R and $g(x)$ is the inverse of $f(x)$ and I have to find out the derivative of $g(x)$ at $x=8$