Mathematics

When you compose two functions, the inverse "undoes" them in reverse order—think of it like putting on socks then shoes, then removing shoes first, then socks. The key insight is that $(f \circ g)^{-1}$ must undo $g$ first (since it was applied last), then undo $f$. This means you're composing the individual inverses, but in the opposite order from the original composition.

When you compose two functions, the inverse "undoes" them in reverse order—think of it like putting on socks then shoes, then removing shoes first, then socks. The key insight is that $(f \circ g)^{-1}$ must undo $g$ first (since it was applied last), then undo $f$. This means you're composing the individual inverses, but in the opposite order from the original composition.