Precalculus Examples

$f (x) = 3 x^{2} - 4 x - 1$ $g (x) = - 2 x + 5$ Find: $((g \circ f)) (x)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x^{2} - 4 x - 1)$ by substituting in the value of $f$ into $g$ .

$g (3 x^{2} - 4 x - 1) = - 2 (3 x^{2} - 4 x - 1) + 5$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (3 x^{2} - 4 x - 1) = - 2 (3 x^{2}) - 2 (- 4 x) - 2 \cdot - 1 + 5$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $3$ by $- 2$ .

$g (3 x^{2} - 4 x - 1) = - 6 x^{2} - 2 (- 4 x) - 2 \cdot - 1 + 5$

Step 3.2.2

Multiply $- 4$ by $- 2$ .

$g (3 x^{2} - 4 x - 1) = - 6 x^{2} + 8 x - 2 \cdot - 1 + 5$

Step 3.2.3

Multiply $- 2$ by $- 1$ .

$g (3 x^{2} - 4 x - 1) = - 6 x^{2} + 8 x + 2 + 5$

Step 4

Add $2$ and $5$ .

$g (3 x^{2} - 4 x - 1) = - 6 x^{2} + 8 x + 7$