Find f(g(x)) f(x)=2/(1-3x) , g(x)=1/x

$f (x) = \frac{2}{1 - 3 x}$ , $g (x) = \frac{1}{x}$

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 $f$ .

$f (\frac{1}{x}) = \frac{2}{1 - 3 \frac{1}{x}}$

Step 3

Simplify the denominator.

Combine $- 3$ and $\frac{1}{x}$ .

$f (\frac{1}{x}) = \frac{2}{1 + \frac{- 3}{x}}$

Move the negative in front of the fraction.

$f (\frac{1}{x}) = \frac{2}{1 - \frac{3}{x}}$

Write $1$ as a fraction with a common denominator.

$f (\frac{1}{x}) = \frac{2}{\frac{x}{x} - \frac{3}{x}}$

Combine the numerators over the common denominator.

$f (\frac{1}{x}) = \frac{2}{\frac{x - 3}{x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{1}{x}) = 2 (\frac{x}{x - 3})$

Step 5

Combine $2$ and $\frac{x}{x - 3}$ .

$f (\frac{1}{x}) = \frac{2 x}{x - 3}$