Find f(g(x)) f(x)=x^2+6x-2 g(x)=x-6

$f (x) = x^{2} + 6 x - 2$ $g (x) = x - 6$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x - 6)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Rewrite ${(x - 6)}^{2}$ as $(x - 6) (x - 6)$ .

$f (x - 6) = (x - 6) (x - 6) + 6 (x - 6) - 2$

Expand $(x - 6) (x - 6)$ using the FOIL Method.

Apply the distributive property.

$f (x - 6) = x (x - 6) - 6 (x - 6) + 6 (x - 6) - 2$

Apply the distributive property.

$f (x - 6) = x \cdot x + x \cdot - 6 - 6 (x - 6) + 6 (x - 6) - 2$

Apply the distributive property.

$f (x - 6) = x \cdot x + x \cdot - 6 - 6 x - 6 \cdot - 6 + 6 (x - 6) - 2$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$f (x - 6) = x^{2} + x \cdot - 6 - 6 x - 6 \cdot - 6 + 6 (x - 6) - 2$

Move $- 6$ to the left of $x$ .

$f (x - 6) = x^{2} - 6 \cdot x - 6 x - 6 \cdot - 6 + 6 (x - 6) - 2$

Multiply $- 6$ by $- 6$ .

$f (x - 6) = x^{2} - 6 x - 6 x + 36 + 6 (x - 6) - 2$

Subtract $6 x$ from $- 6 x$ .

$f (x - 6) = x^{2} - 12 x + 36 + 6 (x - 6) - 2$

Apply the distributive property.

$f (x - 6) = x^{2} - 12 x + 36 + 6 x + 6 \cdot - 6 - 2$

Multiply $6$ by $- 6$ .

$f (x - 6) = x^{2} - 12 x + 36 + 6 x - 36 - 2$

Step 4

Simplify by adding terms.

Combine the opposite terms in $x^{2} - 12 x + 36 + 6 x - 36 - 2$ .

Subtract $36$ from $36$ .

$f (x - 6) = x^{2} - 12 x + 6 x + 0 - 2$

Add $x^{2} - 12 x + 6 x$ and $0$ .

$f (x - 6) = x^{2} - 12 x + 6 x - 2$

Add $- 12 x$ and $6 x$ .

$f (x - 6) = x^{2} - 6 x - 2$