Find f(g(x)) f(x)=(x-5)/3 , g(x)=1/x

$f (x) = \frac{x - 5}{3}$ , $g (x) = \frac{1}{x}$

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 $f$ .

$f (\frac{1}{x}) = \frac{(\frac{1}{x}) - 5}{3}$

Step 3

Simplify the numerator.

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{x}{x}$ .

$f (\frac{1}{x}) = \frac{\frac{1}{x} - 5 \cdot \frac{x}{x}}{3}$

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

$f (\frac{1}{x}) = \frac{\frac{1}{x} + \frac{- 5 x}{x}}{3}$

Combine the numerators over the common denominator.

$f (\frac{1}{x}) = \frac{\frac{1 - 5 x}{x}}{3}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$f (\frac{1}{x}) = \frac{1 - 5 x}{x} \cdot \frac{1}{3}$

Step 5

Multiply $\frac{1 - 5 x}{x}$ by $\frac{1}{3}$ .

$f (\frac{1}{x}) = \frac{1 - 5 x}{x \cdot 3}$

Step 6

Move $3$ to the left of $x$ .

$f (\frac{1}{x}) = \frac{1 - 5 x}{3 x}$