Calculus Examples

$f (y) = y^{2}$ , $g (y) = y + 2$

Step 1

Set up the composite result function.

$f (g (y))$

Step 2

Evaluate $f (y + 2)$ by substituting in the value of $g$ into $f$ .

$f (y + 2) = {(y + 2)}^{2}$

Step 3

Rewrite ${(y + 2)}^{2}$ as $(y + 2) (y + 2)$ .

$f (y + 2) = (y + 2) (y + 2)$

Step 4

Expand $(y + 2) (y + 2)$ using the FOIL Method.

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Step 4.1

Apply the distributive property.

$f (y + 2) = y (y + 2) + 2 (y + 2)$

Step 4.2

Apply the distributive property.

$f (y + 2) = y \cdot y + y \cdot 2 + 2 (y + 2)$

Step 4.3

Apply the distributive property.

$f (y + 2) = y \cdot y + y \cdot 2 + 2 y + 2 \cdot 2$

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

Multiply $y$ by $y$ .

$f (y + 2) = y^{2} + y \cdot 2 + 2 y + 2 \cdot 2$

Step 5.1.2

Move $2$ to the left of $y$ .

$f (y + 2) = y^{2} + 2 \cdot y + 2 y + 2 \cdot 2$

Step 5.1.3

Multiply $2$ by $2$ .

$f (y + 2) = y^{2} + 2 y + 2 y + 4$

Step 5.2

Add $2 y$ and $2 y$ .

$f (y + 2) = y^{2} + 4 y + 4$