How do i find the values of these functions?

Question

Suppose $f$ and $g$ are one-to-one functions such that $f(2)=7$, $f(4)=2$, and $g(2)=5$. If possible, find the values of

A) $(g \circ f^{-1})(7)$

B) $(f \circ g^{-1})(5)$

C) $(f^{-1} \circ g^{-1})(5)$.

Answer 1

A) We know that $f^{-1}(7)=2$ since $f$ is one-to-one. So $g(f^{-1}(7))=g(2)=5$.

B) We know that $g^{-1}(5)=2$ since $g$ is one-to-one. So $f(g^{-1}(5))=f(2)=7$.

C) We know that $f^{-1}(2)=4$ since $f$ is one-to-one. So $f^{-1}(g^{-1}(5))=f^{-1}(2)=4$.