Find f(g(x)) f(x)=x^2 , g(x)=x+20

$f (x) = x^{2}$ , $g (x) = x + 20$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 20)$ by substituting in the value of $g$ into $f$ .

$f (x + 20) = {(x + 20)}^{2}$

Step 3

Rewrite ${(x + 20)}^{2}$ as $(x + 20) (x + 20)$ .

$f (x + 20) = (x + 20) (x + 20)$

Step 4

Expand $(x + 20) (x + 20)$ using the FOIL Method.

Apply the distributive property.

$f (x + 20) = x (x + 20) + 20 (x + 20)$

Apply the distributive property.

$f (x + 20) = x \cdot x + x \cdot 20 + 20 (x + 20)$

Apply the distributive property.

$f (x + 20) = x \cdot x + x \cdot 20 + 20 x + 20 \cdot 20$

Step 5

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$f (x + 20) = x^{2} + x \cdot 20 + 20 x + 20 \cdot 20$

Move $20$ to the left of $x$ .

$f (x + 20) = x^{2} + 20 \cdot x + 20 x + 20 \cdot 20$

Multiply $20$ by $20$ .

$f (x + 20) = x^{2} + 20 x + 20 x + 400$

Add $20 x$ and $20 x$ .

$f (x + 20) = x^{2} + 40 x + 400$