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

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

Set up the composite result function.

$g (f (x))$

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

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

Simplify each term.

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

$g (11 - x) = 9 - ((11 - x) (11 - x))$

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

Apply the distributive property.

$g (11 - x) = 9 - (11 (11 - x) - x (11 - x))$

Apply the distributive property.

$g (11 - x) = 9 - (11 \cdot 11 + 11 (- x) - x (11 - x))$

Apply the distributive property.

$g (11 - x) = 9 - (11 \cdot 11 + 11 (- x) - x \cdot 11 - x (- x))$

Simplify and combine like terms.

Simplify each term.

Multiply $11$ by $11$ .

$g (11 - x) = 9 - (121 + 11 (- x) - x \cdot 11 - x (- x))$

Multiply $- 1$ by $11$ .

$g (11 - x) = 9 - (121 - 11 x - x \cdot 11 - x (- x))$

Multiply $11$ by $- 1$ .

$g (11 - x) = 9 - (121 - 11 x - 11 x - x (- x))$

Rewrite using the commutative property of multiplication.

$g (11 - x) = 9 - (121 - 11 x - 11 x - 1 \cdot (- 1 x \cdot x))$

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

Move $x$ .

$g (11 - x) = 9 - (121 - 11 x - 11 x - 1 \cdot (- 1 (x \cdot x)))$

Multiply $x$ by $x$ .

$g (11 - x) = 9 - (121 - 11 x - 11 x - 1 \cdot (- 1 x^{2}))$

Multiply $- 1$ by $- 1$ .

$g (11 - x) = 9 - (121 - 11 x - 11 x + 1 x^{2})$

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

$g (11 - x) = 9 - (121 - 11 x - 11 x + x^{2})$

Subtract $11 x$ from $- 11 x$ .

$g (11 - x) = 9 - (121 - 22 x + x^{2})$

Apply the distributive property.

$g (11 - x) = 9 - 1 \cdot 121 - (- 22 x) - x^{2}$

Simplify.

Multiply $- 1$ by $121$ .

$g (11 - x) = 9 - 121 - (- 22 x) - x^{2}$

Multiply $- 22$ by $- 1$ .

$g (11 - x) = 9 - 121 + 22 x - x^{2}$

Simplify the expression.

Subtract $121$ from $9$ .

$g (11 - x) = - 112 + 22 x - x^{2}$

Move $- 112$ .

$g (11 - x) = 22 x - x^{2} - 112$

Reorder $22 x$ and $- x^{2}$ .

$g (11 - x) = - x^{2} + 22 x - 112$

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

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