Algebra Examples

$f (x) = 7 x + 11$ $g (x) = - 2 x + 3$ $h (x) = 3 x^{2} + 1$ $(h - g) (x)$

Step 1

Evaluate $h - g$ .

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Step 1.1

Replace the function designators in $h - g$ with the actual functions.

$(3 x^{2} + 1) - (- 2 x + 3)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Multiply $- 2$ by $- 1$ .

$3 x^{2} + 1 + 2 x - 1 \cdot 3$

Step 1.2.3

Multiply $- 1$ by $3$ .

$3 x^{2} + 1 + 2 x - 3$

Step 1.3

Subtract $3$ from $1$ .

$3 x^{2} + 2 x - 2$

Step 2

Evaluate $h - g$ at $x$ .

$3 {(x)}^{2} + 2 (x) - 2$

Step 3

Simplify $3 {(x)}^{2} + 2 (x) - 2$ .

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Step 3.1

Remove parentheses.

$3 {(x)}^{2} + 2 (x) - 2$

Step 3.2

Multiply $2$ by $x$ .

$3 x^{2} + 2 x - 2$