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

Question

Defining New functions Algebraicially

4918 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-17T20:50:07

$f (g (x)) = \frac{1}{6} x$ $f(g(x))=1/6x$ and $g (f (x)) = \frac{1}{6} x$ $g(f(x))=1/6x$ . The domain is $(- \infty, \infty)$ $(-oo,oo)$ .

$f (x) = \frac{1}{2} x$ $f(x)=1/2x$ and $g (x) = \frac{1}{3} x$ $g(x)=1/3x$

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

$f (g (x)) = \frac{1}{2} (\frac{1}{3} x) = \frac{1}{6} x$ $f(g(x))=1/2(1/3x) =1/6x$

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

$g (f (x)) = \frac{1}{3} (\frac{1}{2} x) = \frac{1}{6} x$ $g(f(x))=1/3(1/2x)=1/6x$

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