We know function and its inverse are mirror image about the line y=x and also that their composition is identity function (y=x again) So I was wondering if there is a link? I tried to look up for graphical interpretation of composition of functions but I couldn't fund any.
2026-03-27 18:14:56.1774635296
Graphical interpretation of composition of functions
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If $(x,f(x))$ is a point of the graph of the invertible function $y=f(x)$, than tha point $(f(x),f^{-1}(f(x)))$ is a point of the graph of its inverse function $f^{-1}$, so, since $f^{-1}(f(x))=x$, any point $(x,f(x))$ has its symmetric point $(f(x),x)$, with respect the line $y=x$ on the graph of the inverse function.
The figure illustrates this fact for the functions $f(x)=e^x$ and $f^{-1}(x)=\ln x$. The two symmetric points on the graphs are $E=(\ln2,e^{ln 2}=2)$ and $F=(2,\ln 2)$.