Problem 99 of 7
Verify that f(x)=1/(x-4) and g(x)=4+1/x are inverse functions by composition.
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compute f(g(x)) and g(f(x)).
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Compute f(g(x)) and g(f(x)) and respect domains.
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Solution
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1. Substitute g(x) into f and simplify.
2. Substitute f(x) into g and simplify.
3. State the domains where each composition is valid.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Checking just one composition unless the prompt explicitly asks for one direction.