How do you find the domain of $f(g(x))$ when $f(x) = 1/(x+3)$ and $g = (-2/x)$ ?

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Answer 1 · 2017-08-03T15:58:32

The domain is $D_f(g(x))=RR-{2/3}$

We have,

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

$g(x)=-2/x$

The composition is

#fog= f(g(x))=f(-2/x)=1/((-2/x)+3)=x/(3x-2)#

So,

$3x-2!=0$ , $x!=2/3$

Therefore the domain of $f(g(x))$ is $D_f(g(x))=RR-{2/3}$

How do you find the domain of f(g(x))f(g(x)) when f(x) = 1/(x+3)f(x) = 1/(x+3) and g = (-2/x)g = (-2/x)?