Question

Which function below is the inverse of f(x) = x2 − 25?

Answer 1

Since \[f^{-1}(f(x)) = x\]\[f(f^{-1}(f(x)))=f(x)\]Let \(u=f(x)\)\[
f(f^{-1}(u))=u
\]

Answer 2

\[
f(f^{-1}(u))=(f^{-1}(u))^2-25=u
\]

Answer 3

At this point you solve for \(f^{-1}(u)\): \[\begin{split}
(f^{-1}(u))^2&=u+25\\
|f^{-1}(u)| &= \sqrt{u+25} \\
f^{-1}(u)&=\pm \sqrt{u+25}
\end{split}
\]

Answer 4

Unfortunately, this isn't a function because it has two outputs, and functions only have on e output.