Precalculus Examples

$f (x) = x + 5$ , $g (x) = 2 x + 5$ , $(f g) (0)$

Step 1

Evaluate $f g$ .

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Step 1.1

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

$(x + 5) (2 x + 5)$

Step 1.2

Expand $(x + 5) (2 x + 5)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x (2 x + 5) + 5 (2 x + 5)$

Step 1.2.2

Apply the distributive property.

$x (2 x) + x \cdot 5 + 5 (2 x + 5)$

Step 1.2.3

Apply the distributive property.

$x (2 x) + x \cdot 5 + 5 (2 x) + 5 \cdot 5$

$x (2 x) + x \cdot 5 + 5 (2 x) + 5 \cdot 5$

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

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot 5 + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 1.3.1.2.1

Move $x$ .

$2 (x \cdot x) + x \cdot 5 + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

$2 x^{2} + x \cdot 5 + 5 (2 x) + 5 \cdot 5$

$2 x^{2} + x \cdot 5 + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.3

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

$2 x^{2} + 5 \cdot x + 5 (2 x) + 5 \cdot 5$

Step 1.3.1.4

Multiply $2$ by $5$ .

$2 x^{2} + 5 x + 10 x + 5 \cdot 5$

Step 1.3.1.5

Multiply $5$ by $5$ .

$2 x^{2} + 5 x + 10 x + 25$

$2 x^{2} + 5 x + 10 x + 25$

Step 1.3.2

Add $5 x$ and $10 x$ .

$2 x^{2} + 15 x + 25$

$2 x^{2} + 15 x + 25$

$2 x^{2} + 15 x + 25$

Step 2

Evaluate $f g$ at $0$ .

$2 {(0)}^{2} + 15 (0) + 25$

Step 3

Simplify $2 {(0)}^{2} + 15 (0) + 25$ .

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Step 3.1

Remove parentheses.

$2 {(0)}^{2} + 15 (0) + 25$

Step 3.2

Simplify each term.

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Step 3.2.1

Raising $0$ to any positive power yields $0$ .

$2 \cdot 0 + 15 (0) + 25$

Step 3.2.2

Multiply $2$ by $0$ .

$0 + 15 (0) + 25$

Step 3.2.3

Multiply $15$ by $0$ .

$0 + 0 + 25$

$0 + 0 + 25$

Step 3.3

Simplify by adding numbers.

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Step 3.3.1

Add $0$ and $0$ .

$0 + 25$

Step 3.3.2

Add $0$ and $25$ .

$25$

$25$

$25$

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