If f(g(x)) = g(f(x)) = x, and g(x) = 2 + In(x + 1), find f(4).

Mathematics

1 answer:

Dmitriy789 [7]3 years ago

5 0

If $f(g(x))=g(f(x))=x$ , then $g$ and $f$ are inverses of one another. So we know $g(f(4))=4$ .

$g(f(4))=2+\ln(f(4)+1)=4$

$\implies\ln(f(4)+1)=2$

$\implies f(4)+1=e^2$

$\implies\boxed{f(4)=e^2-1}$

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Step-by-step explanation:

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