Find f(g(x)) f(x)=1/(x-9) , g(x)=1/x

$f (x) = \frac{1}{x - 9}$ , $g (x) = \frac{1}{x}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

$f (\frac{1}{x}) = \frac{1}{(\frac{1}{x}) - 9}$

Step 3

Simplify the denominator.

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$f (\frac{1}{x}) = \frac{1}{\frac{1}{x} - 9 \cdot \frac{x}{x}}$

Combine $- 9$ and $\frac{x}{x}$ .

$f (\frac{1}{x}) = \frac{1}{\frac{1}{x} + \frac{- 9 x}{x}}$

Combine the numerators over the common denominator.

$f (\frac{1}{x}) = \frac{1}{\frac{1 - 9 x}{x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{1}{x}) = 1 (\frac{x}{1 - 9 x})$

Step 5

Multiply $\frac{x}{1 - 9 x}$ by $1$ .

$f (\frac{1}{x}) = \frac{x}{1 - 9 x}$