# 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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