How do you find (g o f)(x) given $f(x)= x/(x-2)$ , $g(x)=3/x$ ?

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Answer 1 · 2015-12-19T19:35:53

$(g@f)(x) = (3x-6)/x$

$(g @ f)(x)$ just means that $g$ is a function of $f(x)$ , so we need to replace $x$ in $g(x)$ with $f(x)$ .

$g(x) = 3/x$

Replace each $x$ with $f(x)$ . In this case, there is only one.

$(g@f)(x) = 3/f(x)$

Now plug in the value of $f(x)$ .

$(g@f)(x) = 3/(x/(x-2))$

Simplify.

$(g@f)(x) = (3(x-2))/x$

$(g@f)(x) = (3x-6)/x$

How do you find (g o f)(x) given f(x)= x/(x-2)f(x)= x/(x-2), g(x)=3/xg(x)=3/x?