Find f(g(x)) f(x)=1/(x-4) , g(x)=2/x+4

$f (x) = \frac{1}{x - 4}$ , $g (x) = \frac{2}{x} + 4$

Set up the composite result function.

$f (g (x))$

Evaluate $f (\frac{2}{x} + 4)$ by substituting in the value of $g$ into $f$ .

$f (\frac{2}{x} + 4) = \frac{1}{(\frac{2}{x} + 4) - 4}$

Simplify the denominator.

Subtract $4$ from $4$ .

$f (\frac{2}{x} + 4) = \frac{1}{\frac{2}{x} + 0}$

Add $\frac{2}{x}$ and $0$ .

$f (\frac{2}{x} + 4) = \frac{1}{\frac{2}{x}}$

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{2}{x} + 4) = 1 (\frac{x}{2})$

Multiply $\frac{x}{2}$ by $1$ .

$f (\frac{2}{x} + 4) = \frac{x}{2}$