Find f(g(x)) f(x)=x^2+4 g(x)=2x+7

$f (x) = x^{2} + 4$ $g (x) = 2 x + 7$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (2 x + 7)$ by substituting in the value of $g$ into $f$ .

$f (2 x + 7) = {(2 x + 7)}^{2} + 4$

Step 3

Simplify each term.

Rewrite ${(2 x + 7)}^{2}$ as $(2 x + 7) (2 x + 7)$ .

$f (2 x + 7) = (2 x + 7) (2 x + 7) + 4$

Expand $(2 x + 7) (2 x + 7)$ using the FOIL Method.

Apply the distributive property.

$f (2 x + 7) = 2 x (2 x + 7) + 7 (2 x + 7) + 4$

Apply the distributive property.

$f (2 x + 7) = 2 x (2 x) + 2 x \cdot 7 + 7 (2 x + 7) + 4$

Apply the distributive property.

$f (2 x + 7) = 2 x (2 x) + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 + 4$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (2 x + 7) = 2 \cdot (2 x \cdot x) + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 + 4$

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

Move $x$ .

$f (2 x + 7) = 2 \cdot (2 (x \cdot x)) + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 + 4$

Multiply $x$ by $x$ .

$f (2 x + 7) = 2 \cdot (2 x^{2}) + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 + 4$

Multiply $2$ by $2$ .

$f (2 x + 7) = 4 x^{2} + 2 x \cdot 7 + 7 (2 x) + 7 \cdot 7 + 4$

Multiply $7$ by $2$ .

$f (2 x + 7) = 4 x^{2} + 14 x + 7 (2 x) + 7 \cdot 7 + 4$

Multiply $2$ by $7$ .

$f (2 x + 7) = 4 x^{2} + 14 x + 14 x + 7 \cdot 7 + 4$

Multiply $7$ by $7$ .

$f (2 x + 7) = 4 x^{2} + 14 x + 14 x + 49 + 4$

Add $14 x$ and $14 x$ .

$f (2 x + 7) = 4 x^{2} + 28 x + 49 + 4$

Step 4

Add $49$ and $4$ .

$f (2 x + 7) = 4 x^{2} + 28 x + 53$