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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (3 x^{2} + x + 5)$ by substituting in the value of $g$ into $f$ .

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

Step 3

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $5$ .

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

Step 4

Subtract $5$ from $3$ .

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