Lets try this with an example.
Suppose we have a function [tex]f(x)=2x[/tex].
Calculate its inverse [tex]f^{-1}(x)=\dfrac{x}{2}[/tex].
And now just simply try to find the composition,
[tex]f(f^{-1}(x))=f\Big(\dfrac{x}{2}\Big)=2\cdot\dfrac{x}{2}=x[/tex].
The answer is the composition of a function and its inverse is always function [tex]g(x)=f(f^{-1}(x))=\boxed{x}[/tex].
Hope this helps.
