Find f(g(x)) f(x)=4-x , g(x)=5-x^2

$f (x) = 4 - x$ , $g (x) = 5 - x^{2}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (5 - x^{2})$ by substituting in the value of $g$ into $f$ .

$f (5 - x^{2}) = 4 - (5 - x^{2})$

Step 3

Simplify each term.

Apply the distributive property.

$f (5 - x^{2}) = 4 - 1 \cdot 5 + x^{2}$

Multiply $- 1$ by $5$ .

$f (5 - x^{2}) = 4 - 5 + x^{2}$

Multiply $- - x^{2}$ .

Multiply $- 1$ by $- 1$ .

$f (5 - x^{2}) = 4 - 5 + 1 x^{2}$

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

$f (5 - x^{2}) = 4 - 5 + x^{2}$

Step 4

Simplify the expression.

Subtract $5$ from $4$ .

$f (5 - x^{2}) = - 1 + x^{2}$

Reorder $- 1$ and $x^{2}$ .

$f (5 - x^{2}) = x^{2} - 1$