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

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

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

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

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

Step 3

Simplify each term.

Apply the distributive property.

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

Simplify.

Multiply $2$ by $- 1$ .

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

Multiply $- 1$ by $2$ .

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

Step 4

Add $- 2$ and $6$ .

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