Find h(g(x)) g(x)=9x-2 h(x)=3x^2+2x

$g (x) = 9 x - 2$ $h (x) = 3 x^{2} + 2 x$

Set up the composite result function.

$h (g (x))$

Evaluate $h (9 x - 2)$ by substituting in the value of $g$ into $h$ .

$h (9 x - 2) = 3 {(9 x - 2)}^{2} + 2 (9 x - 2)$

Simplify each term.

Rewrite ${(9 x - 2)}^{2}$ as $(9 x - 2) (9 x - 2)$ .

$h (9 x - 2) = 3 ((9 x - 2) (9 x - 2)) + 2 (9 x - 2)$

Expand $(9 x - 2) (9 x - 2)$ using the FOIL Method.

Apply the distributive property.

$h (9 x - 2) = 3 (9 x (9 x - 2) - 2 (9 x - 2)) + 2 (9 x - 2)$

Apply the distributive property.

$h (9 x - 2) = 3 (9 x (9 x) + 9 x \cdot - 2 - 2 (9 x - 2)) + 2 (9 x - 2)$

Apply the distributive property.

$h (9 x - 2) = 3 (9 x (9 x) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2) + 2 (9 x - 2)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$h (9 x - 2) = 3 (9 \cdot (9 x \cdot x) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2) + 2 (9 x - 2)$

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

Move $x$ .

$h (9 x - 2) = 3 (9 \cdot (9 (x \cdot x)) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2) + 2 (9 x - 2)$

Multiply $x$ by $x$ .

$h (9 x - 2) = 3 (9 \cdot (9 x^{2}) + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2) + 2 (9 x - 2)$

Multiply $9$ by $9$ .

$h (9 x - 2) = 3 (81 x^{2} + 9 x \cdot - 2 - 2 (9 x) - 2 \cdot - 2) + 2 (9 x - 2)$

Multiply $- 2$ by $9$ .

$h (9 x - 2) = 3 (81 x^{2} - 18 x - 2 (9 x) - 2 \cdot - 2) + 2 (9 x - 2)$

Multiply $9$ by $- 2$ .

$h (9 x - 2) = 3 (81 x^{2} - 18 x - 18 x - 2 \cdot - 2) + 2 (9 x - 2)$

Multiply $- 2$ by $- 2$ .

$h (9 x - 2) = 3 (81 x^{2} - 18 x - 18 x + 4) + 2 (9 x - 2)$

Subtract $18 x$ from $- 18 x$ .

$h (9 x - 2) = 3 (81 x^{2} - 36 x + 4) + 2 (9 x - 2)$

Apply the distributive property.

$h (9 x - 2) = 3 (81 x^{2}) + 3 (- 36 x) + 3 \cdot 4 + 2 (9 x - 2)$

Simplify.

Multiply $81$ by $3$ .

$h (9 x - 2) = 243 x^{2} + 3 (- 36 x) + 3 \cdot 4 + 2 (9 x - 2)$

Multiply $- 36$ by $3$ .

$h (9 x - 2) = 243 x^{2} - 108 x + 3 \cdot 4 + 2 (9 x - 2)$

Multiply $3$ by $4$ .

$h (9 x - 2) = 243 x^{2} - 108 x + 12 + 2 (9 x - 2)$

Apply the distributive property.

$h (9 x - 2) = 243 x^{2} - 108 x + 12 + 2 (9 x) + 2 \cdot - 2$

Multiply $9$ by $2$ .

$h (9 x - 2) = 243 x^{2} - 108 x + 12 + 18 x + 2 \cdot - 2$

Multiply $2$ by $- 2$ .

$h (9 x - 2) = 243 x^{2} - 108 x + 12 + 18 x - 4$

Simplify by adding terms.

Add $- 108 x$ and $18 x$ .

$h (9 x - 2) = 243 x^{2} - 90 x + 12 - 4$

Subtract $4$ from $12$ .

$h (9 x - 2) = 243 x^{2} - 90 x + 8$

Find h(g(x)) g(x)=9x-2 h(x)=3x^2+2x

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