Find f(g(x)) f(x)=x^2+x-1 , g(x)=x+3

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 3)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Remove parentheses.

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

Step 4

Simplify each term.

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

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

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $3$ to the left of $x$ .

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

Multiply $3$ by $3$ .

$f (x + 3) = x^{2} + 3 x + 3 x + 9 + x + 3 - 1$

Add $3 x$ and $3 x$ .

$f (x + 3) = x^{2} + 6 x + 9 + x + 3 - 1$

Step 5

Simplify by adding terms.

Add $6 x$ and $x$ .

$f (x + 3) = x^{2} + 7 x + 9 + 3 - 1$

Simplify by adding and subtracting.

Add $9$ and $3$ .

$f (x + 3) = x^{2} + 7 x + 12 - 1$

Subtract $1$ from $12$ .

$f (x + 3) = x^{2} + 7 x + 11$