A2.F.2.2: Combine functions by com position and recognize that 𝑔(𝑥) = 𝑓^-1(𝑥), the inverse function of 𝑓(𝑥), if and only if 𝑓(𝑔(𝑥)) = 𝑔(𝑓(𝑥)) = 𝑥.

Combine functions by com position and recognize that 𝑔(𝑥) = 𝑓^-1(𝑥), the inverse function of 𝑓(𝑥), if and only if 𝑓(𝑔(𝑥)) = 𝑔(𝑓(𝑥)) = 𝑥.

Example Problems

h(x) = \ln(x)

k(x) = e^x

Evaluate:

h(k(2))

m(x) = x^3

n(x) = \sqrt{x}

Evaluate:

n(m(2))

f(m) = m^3 - m

g(m) = m + 4

Evaluate:

f(g(2))

Khan Academy Resources

Verifying inverse functions by composition Composite and inverse functions: FAQ Verify inverse functions Find composite functions Verifying inverse functions by composition Finding composite functions Verifying inverse functions from tables Verifying inverse functions by composition: not inverse

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