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

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

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

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

Step 3

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $6$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Combine the opposite terms in $x - 3 + 3$ .

Add $- 3$ and $3$ .

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

Add $x$ and $0$ .

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