College Algebra / Unit 5 Alg 296 short lesson, about 20 seconds
The Composition Test for Inverses
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The idea
Two functions are inverses exactly when each undoes the other under composition: f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for every x in the right domain.
In practice
With f(x) = 2x + 3 and f⁻¹(x) = (x − 3)/2: f(f⁻¹(11)) = f(4) = 11, and f⁻¹(f(4)) = f⁻¹(11) = 4.
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