Precalculus Examples

If $f (x) = \frac{1}{x}$ and $g (x) = 3 x + 2$ find $((g \circ g)) (- 4)$

Step 1

Set up the composite result function.

$g (g (x))$

Step 2

Evaluate $g (3 x + 2)$ by substituting in the value of $g$ into $g$ .

$g (3 x + 2) = 3 (3 x + 2) + 2$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (3 x + 2) = 3 (3 x) + 3 \cdot 2 + 2$

Step 3.2

Multiply $3$ by $3$ .

$g (3 x + 2) = 9 x + 3 \cdot 2 + 2$

Step 3.3

Multiply $3$ by $2$ .

$g (3 x + 2) = 9 x + 6 + 2$

Step 4

Add $6$ and $2$ .

$g (3 x + 2) = 9 x + 8$

Step 5

Evaluate the result function by replacing $x$ with $- 4$ in the function.

$9 (- 4) + 8$

Step 6

Simplify the evaluated function.

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Step 6.1

Multiply $9$ by $- 4$ .

$- 36 + 8$

Step 6.2

Add $- 36$ and $8$ .

$- 28$