How do you prove that the function x ⋅ x - 2 x - 2 is not continuous at x=2?

If a function is not defined at some point, the function is not continuous at that point.Division of 0 by 0 is undefinedThe function f ( x ) = x ⋅ x - 2 x - 2 contains a term x - 2 x - 2 which is equivalent to 0 0 when x = 2 and therefore the function is not continuous at x = 2 Note that, in this case, we have what is called a "removal discontinuity" but it is still a discontinuity.

Expert Answer to "How do you prove that the function x..."

College
Calculus and Analysis
Differential Calculus
Continuity

Aldo Ashley

Answered question

2022-10-30

How do you prove that the function

x \cdot \frac{x - 2}{x - 2}

is not continuous at x=2?

Answer & Explanation

fitte8b

Beginner2022-10-31Added 12 answers

If a function is not defined at some point, the function is not continuous at that point.
Division of 0 by 0 is undefined
The function

f (x) = x \cdot \frac{x - 2}{x - 2}

contains a term

\frac{x - 2}{x - 2}

which is equivalent to

\frac{0}{0}

when

x = 2

and therefore the function is not continuous at

x = 2

Note that, in this case, we have what is called a "removal discontinuity" but it is still a discontinuity.

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