Algebra Examples

$f (x) = \frac{1}{x - 7}$ , $g (x) = \frac{4}{x} + 7$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{1}{x - 7})$ by substituting in the value of $f$ into $g$ .

$g (\frac{1}{x - 7}) = \frac{4}{\frac{1}{x - 7}} + 7$

Step 3

Simplify each term.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$g (\frac{1}{x - 7}) = 4 (x - 7) + 7$

Step 3.2

Apply the distributive property.

$g (\frac{1}{x - 7}) = 4 x + 4 \cdot - 7 + 7$

Step 3.3

Multiply $4$ by $- 7$ .

$g (\frac{1}{x - 7}) = 4 x - 28 + 7$

Step 4

Add $- 28$ and $7$ .

$g (\frac{1}{x - 7}) = 4 x - 21$