Let $f(x) = 1 /(x+3)$ and $g(x) = -2 /x$ , how do you find each of the compositions?

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Answer 1 · 2018-07-12T12:41:04

Please see the explanation below.

The functions are

$f(x)=1/(x+3)$

And

$g(x)=-2/x$

There are $2$ compositions

$fog(x)=f(g(x))=f(-2/x)$

$=1/((-2/x)+3)$

$=x/(3x-2)$

And

$gof(x)=g(f(x))=g(1/(x+3))$

$=-2/(1/(x+3))$

$=-2(x+3)$

Therefore,

$fog(x)!=gof(x)$

Let f(x) = 1 /(x+3)f(x) = 1 /(x+3) and g(x) = -2 /xg(x) = -2 /x, how do you find each of the compositions?