Exercises: (+) Verify by Composition That One Function Is the Inverse of Another

Work through each section in order. For every verification problem, check BOTH compositions: f(g(x)) and g(f(x)).

Grade 9·20 problems·~28 min·Common Core Math - HS Functions·standard·hsf-bf-b-4b

Work through problems with immediate feedback

Warm-Up: Review What You Know

What condition must hold for two functions $f$ and $g$ to be inverses of each other?

Only $f(g(x)) = x$ must hold

Only $g(f(x)) = x$ must hold

Both $f(g(x)) = x$ AND $g(f(x)) = x$ must hold

$f(g(x)) = g(f(x))$ must hold (they must be equal to each other, not necessarily to $x$ )