Examples

f (x) = x^{2} + 2 x + 1

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

g (x) = x

$g (x) = x$

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

$f (x) - g x$ .

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

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

Step 1.2

Subtract

x

$x$ from

2 x

$2 x$ .

x^{2} + x + 1

$x^{2} + x + 1$

x^{2} + x + 1

$x^{2} + x + 1$

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)

$(- \infty, \infty)$

Set-Builder Notation:

{x | x \in R}

${x | x \in ℝ}$

Step 3

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