Find g(f(x)) f(x)=x^2+9x g(x)=1/x

$f (x) = x^{2} + 9 x$ $g (x) = \frac{1}{x}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} + 9 x)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} + 9 x) = \frac{1}{x^{2} + 9 x}$

Step 3

Factor $x$ out of $x^{2} + 9 x$ .

Factor $x$ out of $x^{2}$ .

$g (x^{2} + 9 x) = \frac{1}{x \cdot x + 9 x}$

Factor $x$ out of $9 x$ .

$g (x^{2} + 9 x) = \frac{1}{x \cdot x + x \cdot 9}$

Factor $x$ out of $x \cdot x + x \cdot 9$ .

$g (x^{2} + 9 x) = \frac{1}{x (x + 9)}$