Find f(g(x)) f(x)=4-x g(x)=4x^2+x+6

$f (x) = 4 - x$ $g (x) = 4 x^{2} + x + 6$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (4 x^{2} + x + 6)$ by substituting in the value of $g$ into $f$ .

$f (4 x^{2} + x + 6) = 4 - (4 x^{2} + x + 6)$

Step 3

Simplify each term.

Apply the distributive property.

$f (4 x^{2} + x + 6) = 4 - (4 x^{2}) - x - 1 \cdot 6$

Simplify.

Multiply $4$ by $- 1$ .

$f (4 x^{2} + x + 6) = 4 - 4 x^{2} - x - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$f (4 x^{2} + x + 6) = 4 - 4 x^{2} - x - 6$

Step 4

Subtract $6$ from $4$ .

$f (4 x^{2} + x + 6) = - 4 x^{2} - x - 2$