Composition of Inverses

Algebra Level 3

Consider the function \(f\) defined for all real numbers: \[f(x)= \begin{cases} x+a & \text{ if } x<8 \\ 3x-1 & \text{ if } x\geq 8. \end{cases} \] If it has an inverse function that is also defined for all real numbers, what is the value of \[(f^{-1}\circ f^{-1})(65)?\]


Details and assumptions

\(a\) is a constant.

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