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

Why is checking only $f(g(x)) = x$ insufficient to conclude that $f$ and $g$ are inverses?

One check is always sufficient for simple functions

There exist function pairs where $f(g(x)) = x$ but $g(f(x)) \neq x$

The second check always gives the same result as the first

Numeric checks are enough — symbolic checks are not required