Find f(g(x)) f(x)=x^2+4x-14 g(x)=-x+4

$f (x) = x^{2} + 4 x - 14$ $g (x) = - x + 4$

Set up the composite result function.

$f (g (x))$

Evaluate $f (- x + 4)$ by substituting in the value of $g$ into $f$ .

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

Simplify each term.

Rewrite ${(- x + 4)}^{2}$ as $(- x + 4) (- x + 4)$ .

$f (- x + 4) = (- x + 4) (- x + 4) + 4 (- x + 4) - 14$

Expand $(- x + 4) (- x + 4)$ using the FOIL Method.

Apply the distributive property.

$f (- x + 4) = - x (- x + 4) + 4 (- x + 4) + 4 (- x + 4) - 14$

Apply the distributive property.

$f (- x + 4) = - x (- x) - x \cdot 4 + 4 (- x + 4) + 4 (- x + 4) - 14$

Apply the distributive property.

$f (- x + 4) = - x (- x) - x \cdot 4 + 4 (- x) + 4 \cdot 4 + 4 (- x + 4) - 14$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (- x + 4) = - 1 \cdot (- 1 x \cdot x) - x \cdot 4 + 4 (- x) + 4 \cdot 4 + 4 (- x + 4) - 14$

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

Move $x$ .

$f (- x + 4) = - 1 \cdot (- 1 (x \cdot x)) - x \cdot 4 + 4 (- x) + 4 \cdot 4 + 4 (- x + 4) - 14$

Multiply $x$ by $x$ .

$f (- x + 4) = - 1 \cdot (- 1 x^{2}) - x \cdot 4 + 4 (- x) + 4 \cdot 4 + 4 (- x + 4) - 14$

Multiply $- 1$ by $- 1$ .

$f (- x + 4) = 1 x^{2} - x \cdot 4 + 4 (- x) + 4 \cdot 4 + 4 (- x + 4) - 14$

Multiply $x^{2}$ by $1$ .

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

Multiply $4$ by $- 1$ .

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

Multiply $- 1$ by $4$ .

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

Multiply $4$ by $4$ .

$f (- x + 4) = x^{2} - 4 x - 4 x + 16 + 4 (- x + 4) - 14$

Subtract $4 x$ from $- 4 x$ .

$f (- x + 4) = x^{2} - 8 x + 16 + 4 (- x + 4) - 14$

Apply the distributive property.

$f (- x + 4) = x^{2} - 8 x + 16 + 4 (- x) + 4 \cdot 4 - 14$

Multiply $- 1$ by $4$ .

$f (- x + 4) = x^{2} - 8 x + 16 - 4 x + 4 \cdot 4 - 14$

Multiply $4$ by $4$ .

$f (- x + 4) = x^{2} - 8 x + 16 - 4 x + 16 - 14$

Simplify by adding terms.

Subtract $4 x$ from $- 8 x$ .

$f (- x + 4) = x^{2} - 12 x + 16 + 16 - 14$

Simplify by adding and subtracting.

Add $16$ and $16$ .

$f (- x + 4) = x^{2} - 12 x + 32 - 14$

Subtract $14$ from $32$ .

$f (- x + 4) = x^{2} - 12 x + 18$

Find f(g(x)) f(x)=x^2+4x-14 g(x)=-x+4

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