Find g(f(x)) f(x)=3/(x-6) , g(x)=3/x+6

$f (x) = \frac{3}{x - 6}$ , $g (x) = \frac{3}{x} + 6$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{3}{x - 6})$ by substituting in the value of $f$ into $g$ .

$g (\frac{3}{x - 6}) = \frac{3}{\frac{3}{x - 6}} + 6$

Step 3

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{3}{x - 6}) = 3 (\frac{x - 6}{3}) + 6$

Cancel the common factor of $3$ .

Cancel the common factor.

$g (\frac{3}{x - 6}) = 3 (\frac{x - 6}{3}) + 6$

Rewrite the expression.

$g (\frac{3}{x - 6}) = x - 6 + 6$

Step 4

Combine the opposite terms in $x - 6 + 6$ .

Add $- 6$ and $6$ .

$g (\frac{3}{x - 6}) = x + 0$

Add $x$ and $0$ .

$g (\frac{3}{x - 6}) = x$