Find g(f(x)) f(x)=3/(x-8) , g(x)=3/x+8

$f (x) = \frac{3}{x - 8}$ , $g (x) = \frac{3}{x} + 8$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{3}{x - 8})$ by substituting in the value of $f$ into $g$ .

$g (\frac{3}{x - 8}) = \frac{3}{\frac{3}{x - 8}} + 8$

Step 3

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{3}{x - 8}) = 3 (\frac{x - 8}{3}) + 8$

Cancel the common factor of $3$ .

Cancel the common factor.

$g (\frac{3}{x - 8}) = 3 (\frac{x - 8}{3}) + 8$

Rewrite the expression.

$g (\frac{3}{x - 8}) = x - 8 + 8$

Step 4

Combine the opposite terms in $x - 8 + 8$ .

Add $- 8$ and $8$ .

$g (\frac{3}{x - 8}) = x + 0$

Add $x$ and $0$ .

$g (\frac{3}{x - 8}) = x$