Find f(g(x)) f(x)=4-x g(x)=2x^2+x+9

$f (x) = 4 - x$ $g (x) = 2 x^{2} + x + 9$

Set up the composite result function.

$f (g (x))$

Evaluate $f (g (x))$ by substituting in the value of $g$ into $f$ .

$f (2 x^{2} + x + 9) = 4 - (2 x^{2} + x + 9)$

Simplify each term.

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Apply the distributive property.

$f (2 x^{2} + x + 9) = 4 - (2 x^{2}) - x - 1 \cdot 9$

Simplify.

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Multiply $2$ by $- 1$ .

$f (2 x^{2} + x + 9) = 4 - 2 x^{2} - x - 1 \cdot 9$

Multiply $- 1$ by $9$ .

$f (2 x^{2} + x + 9) = 4 - 2 x^{2} - x - 9$

Subtract $9$ from $4$ .

$f (2 x^{2} + x + 9) = - 2 x^{2} - x - 5$

Find f(g(x)) f(x)=4-x g(x)=2x^2+x+9

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