Mathematics

The key insight is that function composition and inverses follow a reversal rule: the inverse of a composition flips the order. Rather than computing both sides separately, recognize that $(h \circ f)^{-1}$ should equal $f^{-1} \circ h^{-1}$ by the composition-reversal property. Your job is to find each function's inverse, apply them in the correct order on the left side, then compose $h$ and $f$ and invert that result on the right side—both should give you the same expression, confirming the rule works here.

The key insight is that function composition and inverses follow a reversal rule: the inverse of a composition flips the order. Rather than computing both sides separately, recognize that $(h \circ f)^{-1}$ should equal $f^{-1} \circ h^{-1}$ by the composition-reversal property. Your job is to find each function's inverse, apply them in the correct order on the left side, then compose $h$ and $f$ and invert that result on the right side—both should give you the same expression, confirming the rule works here.