Algebra Examples

$f (x) = x^{2} - 1$ ; $g (x) = \sqrt{x + 2}$

Step 1

Find the product of the functions.

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Step 1.1

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

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

Step 1.2

Simplify.

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Step 1.2.1

Apply the distributive property.

$x^{2} \sqrt{x + 2} - 1 \sqrt{x + 2}$

Step 1.2.2

Rewrite $- 1 \sqrt{x + 2}$ as $- \sqrt{x + 2}$ .

$x^{2} \sqrt{x + 2} - \sqrt{x + 2}$

Step 2

Set the radicand in $\sqrt{x + 2}$ greater than or equal to $0$ to find where the expression is defined.

$x + 2 \geq 0$

Step 3

Subtract $2$ from both sides of the inequality.

$x \geq - 2$

Step 4

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[- 2, \infty)$

Set-Builder Notation:

${x | x \geq - 2}$

Step 5