Precalculus Examples

$f (x) = 3 - 2 x$ , $g (x) = 3 x^{2} + 2$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 - 2 x)$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

$g (3 - 2 x) = 3 ((3 - 2 x) (3 - 2 x)) + 2$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Apply the distributive property.

$g (3 - 2 x) = 3 (3 (3 - 2 x) - 2 x (3 - 2 x)) + 2$

Step 3.2.2

Apply the distributive property.

$g (3 - 2 x) = 3 (3 \cdot 3 + 3 (- 2 x) - 2 x (3 - 2 x)) + 2$

Step 3.2.3

Apply the distributive property.

$g (3 - 2 x) = 3 (3 \cdot 3 + 3 (- 2 x) - 2 x \cdot 3 - 2 x (- 2 x)) + 2$

Step 3.3

Simplify and combine like terms.

Tap for more steps...

Step 3.3.1

Simplify each term.

Tap for more steps...

Step 3.3.1.1

Multiply $3$ by $3$ .

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

Step 3.3.1.2

Multiply $- 2$ by $3$ .

$g (3 - 2 x) = 3 (9 - 6 x - 2 x \cdot 3 - 2 x (- 2 x)) + 2$

Step 3.3.1.3

Multiply $3$ by $- 2$ .

$g (3 - 2 x) = 3 (9 - 6 x - 6 x - 2 x (- 2 x)) + 2$

Step 3.3.1.4

Rewrite using the commutative property of multiplication.

$g (3 - 2 x) = 3 (9 - 6 x - 6 x - 2 \cdot (- 2 x \cdot x)) + 2$

Step 3.3.1.5

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

Tap for more steps...

Step 3.3.1.5.1

Move $x$ .

$g (3 - 2 x) = 3 (9 - 6 x - 6 x - 2 \cdot (- 2 (x \cdot x))) + 2$

Step 3.3.1.5.2

Multiply $x$ by $x$ .

$g (3 - 2 x) = 3 (9 - 6 x - 6 x - 2 \cdot (- 2 x^{2})) + 2$

Step 3.3.1.6

Multiply $- 2$ by $- 2$ .

$g (3 - 2 x) = 3 (9 - 6 x - 6 x + 4 x^{2}) + 2$

Step 3.3.2

Subtract $6 x$ from $- 6 x$ .

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

Step 3.4

Apply the distributive property.

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

Step 3.5

Simplify.

Tap for more steps...

Step 3.5.1

Multiply $3$ by $9$ .

$g (3 - 2 x) = 27 + 3 (- 12 x) + 3 (4 x^{2}) + 2$

Step 3.5.2

Multiply $- 12$ by $3$ .

$g (3 - 2 x) = 27 - 36 x + 3 (4 x^{2}) + 2$

Step 3.5.3

Multiply $4$ by $3$ .

$g (3 - 2 x) = 27 - 36 x + 12 x^{2} + 2$

Step 4

Simplify the expression.

Tap for more steps...

Step 4.1

Add $27$ and $2$ .

$g (3 - 2 x) = - 36 x + 12 x^{2} + 29$

Step 4.2

Reorder $- 36 x$ and $12 x^{2}$ .

$g (3 - 2 x) = 12 x^{2} - 36 x + 29$