Precalculus Examples

$f (x) = x^{2} - 3 x + 9$ $g (x) = 5 x - 9$ Find: $((g \circ f)) (x)$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - 3 x + 9)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - 3 x + 9) = 5 (x^{2} - 3 x + 9) - 9$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (x^{2} - 3 x + 9) = 5 x^{2} + 5 (- 3 x) + 5 \cdot 9 - 9$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $- 3$ by $5$ .

$g (x^{2} - 3 x + 9) = 5 x^{2} - 15 x + 5 \cdot 9 - 9$

Step 3.2.2

Multiply $5$ by $9$ .

$g (x^{2} - 3 x + 9) = 5 x^{2} - 15 x + 45 - 9$

Step 4

Subtract $9$ from $45$ .

$g (x^{2} - 3 x + 9) = 5 x^{2} - 15 x + 36$