Assume that the function f is a one-to-one function
If f(6)=4, find f^−1(4).
and
The same thing but when given the inverse:
If f^−1(−2)=−5, find f(−5).
Use the definition of "inverse function", of course! That is, if y= f(x) , then $\displaystyle x= f^{-1}(y)$. If $\displaystyle 4= f(6)$, that is, x= 6 and y= 4, $\displaystyle f^{-1}(y)= f^{-1}(y)= x= ?$.
Of course, if $\displaystyle x= f^{-1}(y)$ then y= f(x) so the other should be easy now.