Find f(g(x)) f(x)=x^2-9x-11 g(x)=11x-4

$f (x) = x^{2} - 9 x - 11$ $g (x) = 11 x - 4$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (11 x - 4)$ by substituting in the value of $g$ into $f$ .

$f (11 x - 4) = {(11 x - 4)}^{2} - 9 (11 x - 4) - 11$

Step 3

Simplify each term.

Rewrite ${(11 x - 4)}^{2}$ as $(11 x - 4) (11 x - 4)$ .

$f (11 x - 4) = (11 x - 4) (11 x - 4) - 9 (11 x - 4) - 11$

Expand $(11 x - 4) (11 x - 4)$ using the FOIL Method.

Apply the distributive property.

$f (11 x - 4) = 11 x (11 x - 4) - 4 (11 x - 4) - 9 (11 x - 4) - 11$

Apply the distributive property.

$f (11 x - 4) = 11 x (11 x) + 11 x \cdot - 4 - 4 (11 x - 4) - 9 (11 x - 4) - 11$

Apply the distributive property.

$f (11 x - 4) = 11 x (11 x) + 11 x \cdot - 4 - 4 (11 x) - 4 \cdot - 4 - 9 (11 x - 4) - 11$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$f (11 x - 4) = 11 \cdot (11 x \cdot x) + 11 x \cdot - 4 - 4 (11 x) - 4 \cdot - 4 - 9 (11 x - 4) - 11$

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

Move $x$ .

$f (11 x - 4) = 11 \cdot (11 (x \cdot x)) + 11 x \cdot - 4 - 4 (11 x) - 4 \cdot - 4 - 9 (11 x - 4) - 11$

Multiply $x$ by $x$ .

$f (11 x - 4) = 11 \cdot (11 x^{2}) + 11 x \cdot - 4 - 4 (11 x) - 4 \cdot - 4 - 9 (11 x - 4) - 11$

Multiply $11$ by $11$ .

$f (11 x - 4) = 121 x^{2} + 11 x \cdot - 4 - 4 (11 x) - 4 \cdot - 4 - 9 (11 x - 4) - 11$

Multiply $- 4$ by $11$ .

$f (11 x - 4) = 121 x^{2} - 44 x - 4 (11 x) - 4 \cdot - 4 - 9 (11 x - 4) - 11$

Multiply $11$ by $- 4$ .

$f (11 x - 4) = 121 x^{2} - 44 x - 44 x - 4 \cdot - 4 - 9 (11 x - 4) - 11$

Multiply $- 4$ by $- 4$ .

$f (11 x - 4) = 121 x^{2} - 44 x - 44 x + 16 - 9 (11 x - 4) - 11$

Subtract $44 x$ from $- 44 x$ .

$f (11 x - 4) = 121 x^{2} - 88 x + 16 - 9 (11 x - 4) - 11$

Apply the distributive property.

$f (11 x - 4) = 121 x^{2} - 88 x + 16 - 9 (11 x) - 9 \cdot - 4 - 11$

Multiply $11$ by $- 9$ .

$f (11 x - 4) = 121 x^{2} - 88 x + 16 - 99 x - 9 \cdot - 4 - 11$

Multiply $- 9$ by $- 4$ .

$f (11 x - 4) = 121 x^{2} - 88 x + 16 - 99 x + 36 - 11$

Step 4

Simplify by adding terms.

Subtract $99 x$ from $- 88 x$ .

$f (11 x - 4) = 121 x^{2} - 187 x + 16 + 36 - 11$

Simplify by adding and subtracting.

Add $16$ and $36$ .

$f (11 x - 4) = 121 x^{2} - 187 x + 52 - 11$

Subtract $11$ from $52$ .

$f (11 x - 4) = 121 x^{2} - 187 x + 41$

Find f(g(x)) f(x)=x^2-9x-11 g(x)=11x-4

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