Find f(g(x)) f(x)=x^2+1 g(x)=x+1

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 1)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $x$ by $1$ .

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

Multiply $x$ by $1$ .

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

Multiply $1$ by $1$ .

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

Add $x$ and $x$ .

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

Step 4

Add $1$ and $1$ .

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