Find g(f(x)) f(x)=x+7 g(x)=x^2+2x-1

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

Set up the composite result function.

$g (f (x))$

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

$g (x + 7) = {(x + 7)}^{2} + 2 (x + 7) - 1$

Simplify each term.

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

$g (x + 7) = (x + 7) (x + 7) + 2 (x + 7) - 1$

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

Apply the distributive property.

$g (x + 7) = x (x + 7) + 7 (x + 7) + 2 (x + 7) - 1$

Apply the distributive property.

$g (x + 7) = x \cdot x + x \cdot 7 + 7 (x + 7) + 2 (x + 7) - 1$

Apply the distributive property.

$g (x + 7) = x \cdot x + x \cdot 7 + 7 x + 7 \cdot 7 + 2 (x + 7) - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$g (x + 7) = x^{2} + x \cdot 7 + 7 x + 7 \cdot 7 + 2 (x + 7) - 1$

Move $7$ to the left of $x$ .

$g (x + 7) = x^{2} + 7 \cdot x + 7 x + 7 \cdot 7 + 2 (x + 7) - 1$

Multiply $7$ by $7$ .

$g (x + 7) = x^{2} + 7 x + 7 x + 49 + 2 (x + 7) - 1$

Add $7 x$ and $7 x$ .

$g (x + 7) = x^{2} + 14 x + 49 + 2 (x + 7) - 1$

Apply the distributive property.

$g (x + 7) = x^{2} + 14 x + 49 + 2 x + 2 \cdot 7 - 1$

Multiply $2$ by $7$ .

$g (x + 7) = x^{2} + 14 x + 49 + 2 x + 14 - 1$

Simplify by adding terms.

Add $14 x$ and $2 x$ .

$g (x + 7) = x^{2} + 16 x + 49 + 14 - 1$

Simplify by adding and subtracting.

Add $49$ and $14$ .

$g (x + 7) = x^{2} + 16 x + 63 - 1$

Subtract $1$ from $63$ .

$g (x + 7) = x^{2} + 16 x + 62$