Question

Let the function $ f(x) $ be defined as $ f(x) = \frac{x - |x|}{x} $, then:

• A. the function is continuous everywhere
• B. the function is not continuous
• C. the function is continuous when $ x < 0 $
• D. the function is continuous for all $ x $ except zero

Hint:

Always check the domain first. If a function's denominator is zero at a point, it cannot be continuous there, regardless of whether the limit exists.

Answer 1

The Correct Option is D