Precalculus Examples

$f (x) = x + 3$ , $g (x) = x + 5$ , $(f g) (x)$

Step 1

Evaluate $f g$ .

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Step 1.1

Replace the function designators in $f g$ with the actual functions.

$(x + 3) (x + 5)$

Step 1.2

Expand $(x + 3) (x + 5)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x (x + 5) + 3 (x + 5)$

Step 1.2.2

Apply the distributive property.

$x \cdot x + x \cdot 5 + 3 (x + 5)$

Step 1.2.3

Apply the distributive property.

$x \cdot x + x \cdot 5 + 3 x + 3 \cdot 5$

$x \cdot x + x \cdot 5 + 3 x + 3 \cdot 5$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 5 + 3 x + 3 \cdot 5$

Step 1.3.1.2

Move $5$ to the left of $x$ .

$x^{2} + 5 \cdot x + 3 x + 3 \cdot 5$

Step 1.3.1.3

Multiply $3$ by $5$ .

$x^{2} + 5 x + 3 x + 15$

$x^{2} + 5 x + 3 x + 15$

Step 1.3.2

Add $5 x$ and $3 x$ .

$x^{2} + 8 x + 15$

$x^{2} + 8 x + 15$

$x^{2} + 8 x + 15$

Step 2

Evaluate $f g$ at $x$ .

${(x)}^{2} + 8 (x) + 15$

Step 3

Simplify ${(x)}^{2} + 8 (x) + 15$ .

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Step 3.1

Remove parentheses.

${(x)}^{2} + 8 (x) + 15$

Step 3.2

Multiply $8$ by $x$ .

$x^{2} + 8 x + 15$

$x^{2} + 8 x + 15$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$