Let $\mathsf{f(x)}$ be a differential and an invertible function, such that $\mathsf{f''(x)>0}$ and $\mathsf{f'(x)>0}$.
Prove that$$\mathsf{ f^{-1}\left(\frac{x_1 + x_2 +x_3}{3} \right) > \frac{f^{-1}(x_1)+f^{-1}(x_2)+f^{-1}(x_3)}{3}}$$
I have no clue, how to start it. I think a graphical solution can be obtained but I am confused about the graph of the inverse function.