Finite Math Examples

$f (x) = x^{2}$ , $g (x) = 6 x - 2$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (6 x - 2)$ by substituting in the value of $g$ into $f$ .

$f (6 x - 2) = {(6 x - 2)}^{2}$

Step 3

Rewrite ${(6 x - 2)}^{2}$ as $(6 x - 2) (6 x - 2)$ .

$f (6 x - 2) = (6 x - 2) (6 x - 2)$

Step 4

Expand $(6 x - 2) (6 x - 2)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$f (6 x - 2) = 6 x (6 x - 2) - 2 (6 x - 2)$

Step 4.2

Apply the distributive property.

$f (6 x - 2) = 6 x (6 x) + 6 x \cdot - 2 - 2 (6 x - 2)$

Step 4.3

Apply the distributive property.

$f (6 x - 2) = 6 x (6 x) + 6 x \cdot - 2 - 2 (6 x) - 2 \cdot - 2$

Step 5

Simplify and combine like terms.

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Step 5.1

Simplify each term.

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Step 5.1.1

Rewrite using the commutative property of multiplication.

$f (6 x - 2) = 6 \cdot (6 x \cdot x) + 6 x \cdot - 2 - 2 (6 x) - 2 \cdot - 2$

Step 5.1.2

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

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Step 5.1.2.1

Move $x$ .

$f (6 x - 2) = 6 \cdot (6 (x \cdot x)) + 6 x \cdot - 2 - 2 (6 x) - 2 \cdot - 2$

Step 5.1.2.2

Multiply $x$ by $x$ .

$f (6 x - 2) = 6 \cdot (6 x^{2}) + 6 x \cdot - 2 - 2 (6 x) - 2 \cdot - 2$

Step 5.1.3

Multiply $6$ by $6$ .

$f (6 x - 2) = 36 x^{2} + 6 x \cdot - 2 - 2 (6 x) - 2 \cdot - 2$

Step 5.1.4

Multiply $- 2$ by $6$ .

$f (6 x - 2) = 36 x^{2} - 12 x - 2 (6 x) - 2 \cdot - 2$

Step 5.1.5

Multiply $6$ by $- 2$ .

$f (6 x - 2) = 36 x^{2} - 12 x - 12 x - 2 \cdot - 2$

Step 5.1.6

Multiply $- 2$ by $- 2$ .

$f (6 x - 2) = 36 x^{2} - 12 x - 12 x + 4$

Step 5.2

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

$f (6 x - 2) = 36 x^{2} - 24 x + 4$