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](x)= 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}#