Finite Math Examples

$(f g) (x) (f g) (4)$ , $f (x) = x - 5$ , $g (x) = x + 8$

Step 1

Evaluate $f g$ .

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Step 1.1

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

$(x - 5) (x + 8)$

Step 1.2

Expand $(x - 5) (x + 8)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x (x + 8) - 5 (x + 8)$

Step 1.2.2

Apply the distributive property.

$x \cdot x + x \cdot 8 - 5 (x + 8)$

Step 1.2.3

Apply the distributive property.

$x \cdot x + x \cdot 8 - 5 x - 5 \cdot 8$

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 $x$ .

$x^{2} + x \cdot 8 - 5 x - 5 \cdot 8$

Step 1.3.1.2

Move $8$ to the left of $x$ .

$x^{2} + 8 \cdot x - 5 x - 5 \cdot 8$

Step 1.3.1.3

Multiply $- 5$ by $8$ .

$x^{2} + 8 x - 5 x - 40$

Step 1.3.2

Subtract $5 x$ from $8 x$ .

$x^{2} + 3 x - 40$

Step 2

Evaluate $f g$ at $x$ .

${(x)}^{2} + 3 (x) - 40$

Step 3

Simplify ${(x)}^{2} + 3 (x) - 40$ .

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Step 3.1

Remove parentheses.

${(x)}^{2} + 3 (x) - 40$

Step 3.2

Multiply $3$ by $x$ .

$x^{2} + 3 x - 40$