Question 24Let $f(x)=x^3+3x+1$ for real $x$. Its inverse exists and is given by $$f^{-1}(x)=\left(\frac{x-a+\sqrt{x^2-bx+c}}2\right)^{1/3}+\left(\frac{x-a-\sqrt{x^2-bx+c}}2\right)^{1/3},$$ where $a,b,c$ are positive constants. Find $a+10b+100c$.