Algebra Examples

$f (x) = \frac{6}{x - 5}$ , $g (x) = \frac{1}{7 x}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{6}{x - 5})$ by substituting in the value of $f$ into $g$ .

$g (\frac{6}{x - 5}) = \frac{1}{7 (\frac{6}{x - 5})}$

Step 3

Combine $7$ and $\frac{6}{x - 5}$ .

$g (\frac{6}{x - 5}) = \frac{1}{\frac{7 \cdot 6}{x - 5}}$

Step 4

Multiply $7$ by $6$ .

$g (\frac{6}{x - 5}) = \frac{1}{\frac{42}{x - 5}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{6}{x - 5}) = 1 (\frac{x - 5}{42})$

Step 6

Multiply $\frac{x - 5}{42}$ by $1$ .

$g (\frac{6}{x - 5}) = \frac{x - 5}{42}$