Answer
It was proved that $f(f^{-1}(x))=f^{-1}(f(x))=x$
Work Step by Step
$f(x)=2x+1$ and $f^{-1}(x)=\dfrac{x-1}{2}$
Substitute $x$ by $f^{-1}(x)$ into $f(x)$ and simplify:
$f(f^{-1}(x))=2\big(\dfrac{x-1}{2}\big)+1=...$
$...=x-1+1=x$
Substitute $x$ by $f(x)$ into $f^{-1}(x)$ and simplify:
$f^{-1}(f(x))=\dfrac{(2x+1)-1}{2}=\dfrac{2x+1-1}{2}=\dfrac{2x}{2}=...$
$...=x$
