Find f(g(x)) f(x)=6/(1-5x) , g(x)=1/x

$f (x) = \frac{6}{1 - 5 x}$ , $g (x) = \frac{1}{x}$

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 $f$ .

$f (\frac{1}{x}) = \frac{6}{1 - 5 \frac{1}{x}}$

Step 3

Simplify the denominator.

Combine $- 5$ and $\frac{1}{x}$ .

$f (\frac{1}{x}) = \frac{6}{1 + \frac{- 5}{x}}$

Move the negative in front of the fraction.

$f (\frac{1}{x}) = \frac{6}{1 - \frac{5}{x}}$

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

$f (\frac{1}{x}) = \frac{6}{\frac{x}{x} - \frac{5}{x}}$

Combine the numerators over the common denominator.

$f (\frac{1}{x}) = \frac{6}{\frac{x - 5}{x}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{1}{x}) = 6 (\frac{x}{x - 5})$

Step 5

Combine $6$ and $\frac{x}{x - 5}$ .

$f (\frac{1}{x}) = \frac{6 x}{x - 5}$