Let $f(x) = 2 -x$ and $f(g(x)) = (2x-3)/x$ , how do you find g(x)?

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Answer 1 · 2015-10-30T00:35:50

I found $g(x)=-3/x$

Consider that when you use $g(x)$ you get:
$f(g(x))=2-g(x)=(2x-3)/x$
so:
$2-g(x)=(2x-3)/x$
$g(x)=2-(2x-3)/x$
$g(x)=(cancel(2x)cancel(-2x)-3)/x=-3/x$

Let f(x) = 2 -xf(x) = 2 -x and f(g(x)) = (2x-3)/xf(g(x)) = (2x-3)/x, how do you find g(x)?