b. Verify by composition that one function is the inverse of another.

Students should know that if we have a function f(x) and its inverse function f^-1(x), finding f^-1(f(x)) or f(f^-1(x)) will give us x as the answer. If two functions f(x) and g(x) follow this pattern, that means f(x) and g(x) are inverses of each other.

Students should make use of this fact to make sure that one function is an inverse of the other. It's always best to calculate both f(g(x)) and g(f(x)) to verify, but most of the time only one of the two will suffice.

Problems often arise when squares and square roots are involved (since , not just x). Students should know that even though this seems nitpicky (and it sort of is), that's just how inverses work and they have to respect that. And if finding inverse functions is anything like finding your soulmate, you can—and should—be nitpicky!