Examples

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

Step 1

Find the difference of the functions.

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Step 1.1

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

$x + 1 - (x + 1)$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

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

Step 1.2.2

Multiply $- 1$ by $1$ .

$x + 1 - x - 1$

Step 1.3

Combine the opposite terms in $x + 1 - x - 1$ .

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Step 1.3.1

Subtract $x$ from $x$ .

$0 + 1 - 1$

Step 1.3.2

Add $0$ and $1$ .

$1 - 1$

Step 1.3.3

Subtract $1$ from $1$ .

$0$

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

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