Find g(f(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.

$g (f (x))$

Step 2

Evaluate $g (64 - x^{2})$ by substituting in the value of $f$ into $g$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Multiply $- 1$ by $64$ .

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

Multiply $- - x^{2}$ .

Multiply $- 1$ by $- 1$ .

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

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

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

Step 4

Simplify the expression.

Subtract $64$ from $8$ .

$g (64 - x^{2}) = - 56 + x^{2}$

Reorder $- 56$ and $x^{2}$ .

$g (64 - x^{2}) = x^{2} - 56$