Find g(h(x)) g(x)=3-x^2 h(x)=4-3x

$g (x) = 3 - x^{2}$ $h (x) = 4 - 3 x$

Step 1

Set up the composite result function.

$g (h (x))$

Step 2

Evaluate $g (4 - 3 x)$ by substituting in the value of $h$ into $g$ .

$g (4 - 3 x) = 3 - {(4 - 3 x)}^{2}$

Step 3

Simplify each term.

Rewrite ${(4 - 3 x)}^{2}$ as $(4 - 3 x) (4 - 3 x)$ .

$g (4 - 3 x) = 3 - ((4 - 3 x) (4 - 3 x))$

Expand $(4 - 3 x) (4 - 3 x)$ using the FOIL Method.

Apply the distributive property.

$g (4 - 3 x) = 3 - (4 (4 - 3 x) - 3 x (4 - 3 x))$

Apply the distributive property.

$g (4 - 3 x) = 3 - (4 \cdot 4 + 4 (- 3 x) - 3 x (4 - 3 x))$

Apply the distributive property.

$g (4 - 3 x) = 3 - (4 \cdot 4 + 4 (- 3 x) - 3 x \cdot 4 - 3 x (- 3 x))$

Simplify and combine like terms.

Simplify each term.

Multiply $4$ by $4$ .

$g (4 - 3 x) = 3 - (16 + 4 (- 3 x) - 3 x \cdot 4 - 3 x (- 3 x))$

Multiply $- 3$ by $4$ .

$g (4 - 3 x) = 3 - (16 - 12 x - 3 x \cdot 4 - 3 x (- 3 x))$

Multiply $4$ by $- 3$ .

$g (4 - 3 x) = 3 - (16 - 12 x - 12 x - 3 x (- 3 x))$

Rewrite using the commutative property of multiplication.

$g (4 - 3 x) = 3 - (16 - 12 x - 12 x - 3 \cdot (- 3 x \cdot x))$

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

Move $x$ .

$g (4 - 3 x) = 3 - (16 - 12 x - 12 x - 3 \cdot (- 3 (x \cdot x)))$

Multiply $x$ by $x$ .

$g (4 - 3 x) = 3 - (16 - 12 x - 12 x - 3 \cdot (- 3 x^{2}))$

Multiply $- 3$ by $- 3$ .

$g (4 - 3 x) = 3 - (16 - 12 x - 12 x + 9 x^{2})$

Subtract $12 x$ from $- 12 x$ .

$g (4 - 3 x) = 3 - (16 - 24 x + 9 x^{2})$

Apply the distributive property.

$g (4 - 3 x) = 3 - 1 \cdot 16 - (- 24 x) - (9 x^{2})$

Simplify.

Multiply $- 1$ by $16$ .

$g (4 - 3 x) = 3 - 16 - (- 24 x) - (9 x^{2})$

Multiply $- 24$ by $- 1$ .

$g (4 - 3 x) = 3 - 16 + 24 x - (9 x^{2})$

Multiply $9$ by $- 1$ .

$g (4 - 3 x) = 3 - 16 + 24 x - 9 x^{2}$

Step 4

Simplify the expression.

Subtract $16$ from $3$ .

$g (4 - 3 x) = - 13 + 24 x - 9 x^{2}$

Move $- 13$ .

$g (4 - 3 x) = 24 x - 9 x^{2} - 13$

Reorder $24 x$ and $- 9 x^{2}$ .

$g (4 - 3 x) = - 9 x^{2} + 24 x - 13$

Find g(h(x)) g(x)=3-x^2 h(x)=4-3x

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