Find the Domain of the Product of the Functions f(x)=x^2-1 , g(x)=2x

$f (x) = x^{2} - 1$ , $g (x) = 2 x$

Step 1

Find the product of the functions.

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

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

Simplify.

Apply the distributive property.

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

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 1$ .

$2 x^{2} x - 2 x$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x^{2}) - 2 x$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

$2 x^{3} - 2 x$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

Find the Domain of the Product of the Functions f(x)=x^2-1 , g(x)=2x

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