F(x)=1/2x; g(x)=1/3x find f(g(x) and g(f(x) State domain of each Precalculus questions?

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Defining New functions Algebraicially

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Answer 1 · 2016-09-17T20:50:07

$f(g(x))=1/6x$ and $g(f(x))=1/6x$ . The domain is $(-oo,oo)$ .

$f(x)=1/2x$ and $g(x)=1/3x$

To find $f(g(x))$ , plug $g(x)$ into $f(x)$

$f(g(x))=1/2(1/3x) =1/6x$

To find $g(f(x))$ , plug $f(x)$ into $g(x)$

$g(f(x))=1/3(1/2x)=1/6x$

The domain of $1/6x$ is $(-oo,oo)$ because f(x) is defined for all values of x.