Question

If f(3)=4, find f^-1(4)......help!!!!

Answer 1

If f is invertible (ie has a unique inverse), then

\[\Large f^{-1}(f(x)) = x\]

for all x in the domain.


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So that means


\[\Large f(3) = 4\]
\[\Large f^{-1}(f(3)) = f^{-1}(4) \ \ {\color{blue}{\text{apply inverse to both sides}}}\]
\[\Large 3 = f^{-1}(4)\]
\[\Large f^{-1}(4) = 3\]