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Precalculus · F-BF

Compose Functions with Their Inverses — f(f⁻¹(x)) = x

If f and g are inverse functions, then f(g(x)) = x and g(f(x)) = x for all x in the domain.

PrecalculusCommon Core HSF-BF.B.4dF-BFVerified correct ✓

Worked examples

Given f(x) = 2x + 0, its inverse is f⁻¹(x) = (x − 0) / 2. Compute f(f⁻¹(-2)) to verify the identity property. What is the result?
Answer: -2
Given f(x) = 3x + 2, its inverse is f⁻¹(x) = (x − 2) / 3. Compute f(f⁻¹(3)) to verify the identity property. What is the result?
Answer: 3

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