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in Inverse Function Property Use the Inverse Function Property to show that $f$ and $g$ are inverses of each other.$$f(x)=\frac{1}{x-1} ; \quad g(x)=\frac{1}{x}+1$$
Step 1
We know that $g(x) = \frac{1}{x} + 1$. Substituting $g(x)$ into $f(x)$, we get: $$f(g(x)) = f\left(\frac{1}{x} + 1\right) = \frac{1}{\left(\frac{1}{x} + 1\right) - 1}.$$ Show more…
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