Solve the Function Operation f(x)=3x-7 , g(x)=-2x-6 , (f*g)(4)

$f (x) = 3 x - 7$ , $g (x) = - 2 x - 6$ , $(f \cdot g) (4)$

Step 1

Evaluate $f \cdot g$ .

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

$(3 x - 7) \cdot (- 2 x - 6)$

Expand $(3 x - 7) (- 2 x - 6)$ using the FOIL Method.

Apply the distributive property.

$3 x (- 2 x - 6) - 7 (- 2 x - 6)$

Apply the distributive property.

$3 x (- 2 x) + 3 x \cdot - 6 - 7 (- 2 x - 6)$

Apply the distributive property.

$3 x (- 2 x) + 3 x \cdot - 6 - 7 (- 2 x) - 7 \cdot - 6$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot - 2 x \cdot x + 3 x \cdot - 6 - 7 (- 2 x) - 7 \cdot - 6$

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

Move $x$ .

$3 \cdot - 2 (x \cdot x) + 3 x \cdot - 6 - 7 (- 2 x) - 7 \cdot - 6$

Multiply $x$ by $x$ .

$3 \cdot - 2 x^{2} + 3 x \cdot - 6 - 7 (- 2 x) - 7 \cdot - 6$

Multiply $3$ by $- 2$ .

$- 6 x^{2} + 3 x \cdot - 6 - 7 (- 2 x) - 7 \cdot - 6$

Multiply $- 6$ by $3$ .

$- 6 x^{2} - 18 x - 7 (- 2 x) - 7 \cdot - 6$

Multiply $- 2$ by $- 7$ .

$- 6 x^{2} - 18 x + 14 x - 7 \cdot - 6$

Multiply $- 7$ by $- 6$ .

$- 6 x^{2} - 18 x + 14 x + 42$

Add $- 18 x$ and $14 x$ .

$- 6 x^{2} - 4 x + 42$

Step 2

Evaluate $f \cdot g$ at $4$ .

$- 6 {(4)}^{2} - 4 \cdot 4 + 42$

Step 3

Simplify $- 6 {(4)}^{2} - 4 \cdot 4 + 42$ .

Remove parentheses.

$- 6 {(4)}^{2} - 4 \cdot 4 + 42$

Simplify each term.

Raise $4$ to the power of $2$ .

$- 6 \cdot 16 - 4 \cdot 4 + 42$

Multiply $- 6$ by $16$ .

$- 96 - 4 \cdot 4 + 42$

Multiply $- 4$ by $4$ .

$- 96 - 16 + 42$

Simplify by adding and subtracting.

Subtract $16$ from $- 96$ .

$- 112 + 42$

Add $- 112$ and $42$ .

$- 70$

Solve the Function Operation f(x)=3x-7 , g(x)=-2x-6 , (f*g)(4)

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