Find g(f(x)) f(x)=x+2 , g(x)=4x^2-7x-2

$f (x) = x + 2$ , $g (x) = 4 x^{2} - 7 x - 2$

Set up the composite result function.

$g (f (x))$

Evaluate $g (x + 2)$ by substituting in the value of $f$ into $g$ .

$g (x + 2) = 4 {(x + 2)}^{2} - 7 (x + 2) - 2$

Simplify each term.

Rewrite ${(x + 2)}^{2}$ as $(x + 2) (x + 2)$ .

$g (x + 2) = 4 ((x + 2) (x + 2)) - 7 (x + 2) - 2$

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

Apply the distributive property.

$g (x + 2) = 4 (x (x + 2) + 2 (x + 2)) - 7 (x + 2) - 2$

Apply the distributive property.

$g (x + 2) = 4 (x \cdot x + x \cdot 2 + 2 (x + 2)) - 7 (x + 2) - 2$

Apply the distributive property.

$g (x + 2) = 4 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) - 7 (x + 2) - 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$g (x + 2) = 4 (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) - 7 (x + 2) - 2$

Move $2$ to the left of $x$ .

$g (x + 2) = 4 (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) - 7 (x + 2) - 2$

Multiply $2$ by $2$ .

$g (x + 2) = 4 (x^{2} + 2 x + 2 x + 4) - 7 (x + 2) - 2$

Add $2 x$ and $2 x$ .

$g (x + 2) = 4 (x^{2} + 4 x + 4) - 7 (x + 2) - 2$

Apply the distributive property.

$g (x + 2) = 4 x^{2} + 4 (4 x) + 4 \cdot 4 - 7 (x + 2) - 2$

Simplify.

Multiply $4$ by $4$ .

$g (x + 2) = 4 x^{2} + 16 x + 4 \cdot 4 - 7 (x + 2) - 2$

Multiply $4$ by $4$ .

$g (x + 2) = 4 x^{2} + 16 x + 16 - 7 (x + 2) - 2$

Apply the distributive property.

$g (x + 2) = 4 x^{2} + 16 x + 16 - 7 x - 7 \cdot 2 - 2$

Multiply $- 7$ by $2$ .

$g (x + 2) = 4 x^{2} + 16 x + 16 - 7 x - 14 - 2$

Simplify by adding terms.

Subtract $7 x$ from $16 x$ .

$g (x + 2) = 4 x^{2} + 9 x + 16 - 14 - 2$

Subtract $14$ from $16$ .

$g (x + 2) = 4 x^{2} + 9 x + 2 - 2$

Combine the opposite terms in $4 x^{2} + 9 x + 2 - 2$ .

Subtract $2$ from $2$ .

$g (x + 2) = 4 x^{2} + 9 x + 0$

Add $4 x^{2} + 9 x$ and $0$ .

$g (x + 2) = 4 x^{2} + 9 x$

Find g(f(x)) f(x)=x+2 , g(x)=4x^2-7x-2

Related Questions

Support LCMGCF.com by disabling your adblocker.