Finite Math Examples

f (x) = 3 x^{2}

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

g (x) = x + 1

$g (x) = x + 1$ ,

(f \circ g)

$(f \circ g)$

Step 1

Set up the composite result function.

f (g (x))

$f (g (x))$

Step 2

Evaluate

f (x + 1)

$f (x + 1)$ by substituting in the value of

g

$g$ into

f

$f$ .

f (x + 1) = 3 {(x + 1)}^{2}

$f (x + 1) = 3 {(x + 1)}^{2}$

Step 3

Rewrite

{(x + 1)}^{2}

${(x + 1)}^{2}$ as

(x + 1) (x + 1)

$(x + 1) (x + 1)$ .

f (x + 1) = 3 ((x + 1) (x + 1))

$f (x + 1) = 3 ((x + 1) (x + 1))$

Step 4

Expand

(x + 1) (x + 1)

$(x + 1) (x + 1)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

f (x + 1) = 3 (x (x + 1) + 1 (x + 1))

$f (x + 1) = 3 (x (x + 1) + 1 (x + 1))$

Step 4.2

Apply the distributive property.

f (x + 1) = 3 (x \cdot x + x \cdot 1 + 1 (x + 1))

$f (x + 1) = 3 (x \cdot x + x \cdot 1 + 1 (x + 1))$

Step 4.3

Apply the distributive property.

f (x + 1) = 3 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1)

$f (x + 1) = 3 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1)$

f (x + 1) = 3 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1)

$f (x + 1) = 3 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1)$

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

Multiply

x

$x$ by

x

$x$ .

f (x + 1) = 3 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1)

$f (x + 1) = 3 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1)$

Step 5.1.2

Multiply

x

$x$ by

1

$1$ .

f (x + 1) = 3 (x^{2} + x + 1 x + 1 \cdot 1)

$f (x + 1) = 3 (x^{2} + x + 1 x + 1 \cdot 1)$

Step 5.1.3

Multiply

x

$x$ by

1

$1$ .

f (x + 1) = 3 (x^{2} + x + x + 1 \cdot 1)

$f (x + 1) = 3 (x^{2} + x + x + 1 \cdot 1)$

Step 5.1.4

Multiply

1

$1$ by

1

$1$ .

f (x + 1) = 3 (x^{2} + x + x + 1)

$f (x + 1) = 3 (x^{2} + x + x + 1)$

f (x + 1) = 3 (x^{2} + x + x + 1)

$f (x + 1) = 3 (x^{2} + x + x + 1)$

Step 5.2

Add

x

$x$ and

x

$x$ .

f (x + 1) = 3 (x^{2} + 2 x + 1)

$f (x + 1) = 3 (x^{2} + 2 x + 1)$

f (x + 1) = 3 (x^{2} + 2 x + 1)

$f (x + 1) = 3 (x^{2} + 2 x + 1)$

Step 6

Apply the distributive property.

f (x + 1) = 3 x^{2} + 3 (2 x) + 3 \cdot 1

$f (x + 1) = 3 x^{2} + 3 (2 x) + 3 \cdot 1$

Step 7

Simplify.

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Step 7.1

Multiply

2

$2$ by

3

$3$ .

f (x + 1) = 3 x^{2} + 6 x + 3 \cdot 1

$f (x + 1) = 3 x^{2} + 6 x + 3 \cdot 1$

Step 7.2

Multiply

3

$3$ by

1

$1$ .

f (x + 1) = 3 x^{2} + 6 x + 3

$f (x + 1) = 3 x^{2} + 6 x + 3$

f (x + 1) = 3 x^{2} + 6 x + 3

$f (x + 1) = 3 x^{2} + 6 x + 3$

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