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

$f (x) = x + 1$ , $g (x) = x - 1$

Step 1

Find the product of the functions.

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

$(x + 1) \cdot (x - 1)$

Simplify.

Expand $(x + 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$x (x - 1) + 1 (x - 1)$

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 1 (x - 1)$

Apply the distributive property.

$x \cdot x + x \cdot - 1 + 1 x + 1 \cdot - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

Move $- 1$ to the left of $x$ .

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

Rewrite $- 1 x$ as $- x$ .

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

Multiply $x$ by $1$ .

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

Multiply $- 1$ by $1$ .

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

Add $- x$ and $x$ .

$x^{2} + 0 - 1$

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

$x^{2} - 1$

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+1 , g(x)=x-1

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