Problem 57 of 7
Verify whether f(x)=x+5 and g(x)=x-4 are inverse functions.
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check f(g(x))=x and g(f(x))=x where appropriate.
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Functions must have compatible domains for inverse verification.
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Solution
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1. Compute f(g(x)) and g(f(x)) when algebraically feasible.
2. Check whether both simplify to x on the relevant domains.
3. Conclude whether they are inverses.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Checking only one example point as proof for all inputs.