Precalculus Examples

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

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} + 3 x - 5)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

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

Step 3.2

Simplify.

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Step 3.2.1

Multiply $3$ by $5$ .

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

Step 3.2.2

Multiply $5$ by $- 5$ .

$g (x^{2} + 3 x - 5) = 5 x^{2} + 15 x - 25 + 2$

Step 4

Add $- 25$ and $2$ .

$g (x^{2} + 3 x - 5) = 5 x^{2} + 15 x - 23$