Find f(g(x)) f(x)=3x+1 , g(x)=5-x^2

$f (x) = 3 x + 1$ , $g (x) = 5 - x^{2}$

Set up the composite result function.

$f (g (x))$

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

$f (5 - x^{2}) = 3 (5 - x^{2}) + 1$

Simplify each term.

Apply the distributive property.

$f (5 - x^{2}) = 3 \cdot 5 + 3 (- x^{2}) + 1$

Multiply $3$ by $5$ .

$f (5 - x^{2}) = 15 + 3 (- x^{2}) + 1$

Multiply $- 1$ by $3$ .

$f (5 - x^{2}) = 15 - 3 x^{2} + 1$

Add $15$ and $1$ .

$f (5 - x^{2}) = - 3 x^{2} + 16$