Precalculus Examples

$f (x) = 7 x + 11$ $g (x) = - 2 x + 3$ $h (x) = 3 x^{2} + 1$ $(f \cdot g) (x)$

Step 1

Evaluate $f \cdot g$ .

Tap for more steps...

Step 1.1

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

$(7 x + 11) \cdot (- 2 x + 3)$

Step 1.2

Expand $(7 x + 11) (- 2 x + 3)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$7 x (- 2 x + 3) + 11 (- 2 x + 3)$

Step 1.2.2

Apply the distributive property.

$7 x (- 2 x) + 7 x \cdot 3 + 11 (- 2 x + 3)$

Step 1.2.3

Apply the distributive property.

$7 x (- 2 x) + 7 x \cdot 3 + 11 (- 2 x) + 11 \cdot 3$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$7 \cdot - 2 x \cdot x + 7 x \cdot 3 + 11 (- 2 x) + 11 \cdot 3$

Step 1.3.1.2

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

Tap for more steps...

Step 1.3.1.2.1

Move $x$ .

$7 \cdot - 2 (x \cdot x) + 7 x \cdot 3 + 11 (- 2 x) + 11 \cdot 3$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

$7 \cdot - 2 x^{2} + 7 x \cdot 3 + 11 (- 2 x) + 11 \cdot 3$

Step 1.3.1.3

Multiply $7$ by $- 2$ .

$- 14 x^{2} + 7 x \cdot 3 + 11 (- 2 x) + 11 \cdot 3$

Step 1.3.1.4

Multiply $3$ by $7$ .

$- 14 x^{2} + 21 x + 11 (- 2 x) + 11 \cdot 3$

Step 1.3.1.5

Multiply $- 2$ by $11$ .

$- 14 x^{2} + 21 x - 22 x + 11 \cdot 3$

Step 1.3.1.6

Multiply $11$ by $3$ .

$- 14 x^{2} + 21 x - 22 x + 33$

Step 1.3.2

Subtract $22 x$ from $21 x$ .

$- 14 x^{2} - x + 33$

Step 2

Evaluate $f \cdot g$ at $x$ .

$- 14 {(x)}^{2} - (x) + 33$

Step 3

Simplify $- 14 {(x)}^{2} - (x) + 33$ .

Tap for more steps...

Step 3.1

Remove parentheses.

$- 14 {(x)}^{2} - (x) + 33$

Step 3.2

Multiply $- 1$ by $x$ .

$- 14 x^{2} - x + 33$