Find g(f(x)) f(x)=2/(x-9) g(x)=2/x+9

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{2}{x - 9})$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Combine the opposite terms in $x - 9 + 9$ .

Add $- 9$ and $9$ .

$g (\frac{2}{x - 9}) = x + 0$

Add $x$ and $0$ .

$g (\frac{2}{x - 9}) = x$