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

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

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Answer 1 · 2015-12-19T19:35:53

$(g \circ f) (x) = \frac{3 x - 6}{x}$ $(g@f)(x) = (3x-6)/x$

Explanation:

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

$g (x) = \frac{3}{x}$ $g(x) = 3/x$

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

$(g \circ f) (x) = \frac{3}{f (x)}$ $(g@f)(x) = 3/f(x)$

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

$(g \circ f) (x) = \frac{3}{\frac{x}{x - 2}}$ $(g@f)(x) = 3/(x/(x-2))$

Simplify.

$(g \circ f) (x) = \frac{3 (x - 2)}{x}$ $(g@f)(x) = (3(x-2))/x$

$(g \circ f) (x) = \frac{3 x - 6}{x}$ $(g@f)(x) = (3x-6)/x$

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

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

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