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

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{x}{x + 1})$ by substituting in the value of $f$ into $g$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Combine $4$ and $\frac{x + 1}{x}$ .

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