Question
Show that $f(g(x))=x$ and $g(f(x))=x$ for all $x:$$f(x)=\frac{1}{x+2} \text { and } g(x)=\frac{1-2 x}{x}(x \neq 0, x \neq-2)$
Step 1
We substitute $g(x)$ into $f(x)$: \[f(g(x))=f\left(\frac{1-2x}{x}\right)=\frac{1}{\frac{1-2x}{x}+2}\] Show more…
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