Solve the Function Operation f(x)=x^2-4x , g(x)=4x+2 , (g*f)(-2)=

$f (x) = x^{2} - 4 x$ , $g (x) = 4 x + 2$ , $(g \cdot f) (- 2)$

Step 1

Evaluate $g \cdot f$ .

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

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

Expand $(4 x + 2) (x^{2} - 4 x)$ using the FOIL Method.

Apply the distributive property.

$4 x (x^{2} - 4 x) + 2 (x^{2} - 4 x)$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$4 (x^{2} x) + 4 x (- 4 x) + 2 x^{2} + 2 (- 4 x)$

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

$4 (x^{2} x^{1}) + 4 x (- 4 x) + 2 x^{2} + 2 (- 4 x)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 x^{2 + 1} + 4 x (- 4 x) + 2 x^{2} + 2 (- 4 x)$

Add $2$ and $1$ .

$4 x^{3} + 4 x (- 4 x) + 2 x^{2} + 2 (- 4 x)$

Rewrite using the commutative property of multiplication.

$4 x^{3} + 4 \cdot - 4 x \cdot x + 2 x^{2} + 2 (- 4 x)$

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

Move $x$ .

$4 x^{3} + 4 \cdot - 4 (x \cdot x) + 2 x^{2} + 2 (- 4 x)$

Multiply $x$ by $x$ .

$4 x^{3} + 4 \cdot - 4 x^{2} + 2 x^{2} + 2 (- 4 x)$

Multiply $4$ by $- 4$ .

$4 x^{3} - 16 x^{2} + 2 x^{2} + 2 (- 4 x)$

Multiply $- 4$ by $2$ .

$4 x^{3} - 16 x^{2} + 2 x^{2} - 8 x$

Add $- 16 x^{2}$ and $2 x^{2}$ .

$4 x^{3} - 14 x^{2} - 8 x$

Step 2

Evaluate $g \cdot f$ at $- 2$ .

$4 {(- 2)}^{3} - 14 {(- 2)}^{2} - 8 \cdot - 2$

Step 3

Simplify $4 {(- 2)}^{3} - 14 {(- 2)}^{2} - 8 \cdot - 2$ .

Remove parentheses.

$4 {(- 2)}^{3} - 14 {(- 2)}^{2} - 8 \cdot - 2$

Simplify each term.

Raise $- 2$ to the power of $3$ .

$4 \cdot - 8 - 14 {(- 2)}^{2} - 8 \cdot - 2$

Multiply $4$ by $- 8$ .

$- 32 - 14 {(- 2)}^{2} - 8 \cdot - 2$

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

$- 32 - 14 \cdot 4 - 8 \cdot - 2$

Multiply $- 14$ by $4$ .

$- 32 - 56 - 8 \cdot - 2$

Multiply $- 8$ by $- 2$ .

$- 32 - 56 + 16$

Simplify by adding and subtracting.

Subtract $56$ from $- 32$ .

$- 88 + 16$

Add $- 88$ and $16$ .

$- 72$

Solve the Function Operation f(x)=x^2-4x , g(x)=4x+2 , (g*f)(-2)=

Related Questions

Support LCMGCF.com by disabling your adblocker.