Find f(g(x)) f(x)=64-x^2 , g(x)=8-x

$f (x) = 64 - x^{2}$ , $g (x) = 8 - x$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (8 - x)$ by substituting in the value of $g$ into $f$ .

$f (8 - x) = 64 - {(8 - x)}^{2}$

Step 3

Simplify each term.

Rewrite ${(8 - x)}^{2}$ as $(8 - x) (8 - x)$ .

$f (8 - x) = 64 - ((8 - x) (8 - x))$

Expand $(8 - x) (8 - x)$ using the FOIL Method.

Apply the distributive property.

$f (8 - x) = 64 - (8 (8 - x) - x (8 - x))$

Apply the distributive property.

$f (8 - x) = 64 - (8 \cdot 8 + 8 (- x) - x (8 - x))$

Apply the distributive property.

$f (8 - x) = 64 - (8 \cdot 8 + 8 (- x) - x \cdot 8 - x (- x))$

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $8$ .

$f (8 - x) = 64 - (64 + 8 (- x) - x \cdot 8 - x (- x))$

Multiply $- 1$ by $8$ .

$f (8 - x) = 64 - (64 - 8 x - x \cdot 8 - x (- x))$

Multiply $8$ by $- 1$ .

$f (8 - x) = 64 - (64 - 8 x - 8 x - x (- x))$

Rewrite using the commutative property of multiplication.

$f (8 - x) = 64 - (64 - 8 x - 8 x - 1 \cdot (- 1 x \cdot x))$

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

Move $x$ .

$f (8 - x) = 64 - (64 - 8 x - 8 x - 1 \cdot (- 1 (x \cdot x)))$

Multiply $x$ by $x$ .

$f (8 - x) = 64 - (64 - 8 x - 8 x - 1 \cdot (- 1 x^{2}))$

Multiply $- 1$ by $- 1$ .

$f (8 - x) = 64 - (64 - 8 x - 8 x + 1 x^{2})$

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

$f (8 - x) = 64 - (64 - 8 x - 8 x + x^{2})$

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

$f (8 - x) = 64 - (64 - 16 x + x^{2})$

Apply the distributive property.

$f (8 - x) = 64 - 1 \cdot 64 - (- 16 x) - x^{2}$

Simplify.

Multiply $- 1$ by $64$ .

$f (8 - x) = 64 - 64 - (- 16 x) - x^{2}$

Multiply $- 16$ by $- 1$ .

$f (8 - x) = 64 - 64 + 16 x - x^{2}$

Step 4

Simplify the expression.

Subtract $64$ from $64$ .

$f (8 - x) = 0 + 16 x - x^{2}$

Add $0$ and $16 x$ .

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

Reorder $16 x$ and $- x^{2}$ .

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

Find f(g(x)) f(x)=64-x^2 , g(x)=8-x

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