I have a continuous function $f(x)$ and I want to find $f^{-1}(3)$, but I can't find $f^{-1}$ directly. I know that $f(1)=3$ and $f'(x)>0$ for all x. Because the function is continuous and always increasing, does that mean that the function necessarily has an inverse and that there is only one value s.t. $f(x)=3$, therefore $f^{-1}(3)=1$?
2026-03-30 03:56:46.1774843006
Determining $f^{-1}(3)$ without knowing $f^{-1}(x)$ but given $f(1)=3$ and $f'(x)>0$.
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