Algebra Examples

$f (x) = x^{2} - x + 7$ $g (x) = - 2 x + 14$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (x^{2} - x + 7)$ by substituting in the value of $f$ into $g$ .

$g (x^{2} - x + 7) = - 2 (x^{2} - x + 7) + 14$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$g (x^{2} - x + 7) = - 2 x^{2} - 2 (- x) - 2 \cdot 7 + 14$

Step 3.2

Simplify.

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Step 3.2.1

Multiply $- 1$ by $- 2$ .

$g (x^{2} - x + 7) = - 2 x^{2} + 2 x - 2 \cdot 7 + 14$

Step 3.2.2

Multiply $- 2$ by $7$ .

$g (x^{2} - x + 7) = - 2 x^{2} + 2 x - 14 + 14$

Step 4

Combine the opposite terms in $- 2 x^{2} + 2 x - 14 + 14$ .

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Step 4.1

Add $- 14$ and $14$ .

$g (x^{2} - x + 7) = - 2 x^{2} + 2 x + 0$

Step 4.2

Add $- 2 x^{2} + 2 x$ and $0$ .

$g (x^{2} - x + 7) = - 2 x^{2} + 2 x$