Question

The number of points of discontinuity of the function \( f(x) = x - [x] \) in the interval \( (0, 7) \) are:

• A. 2
• B. 3
• C. 6
• D. 4

Hint:

Discontinuities in fractional part functions occur at integer values, where the function jumps.

Answer 1

The Correct Option is C

Step 1: The function \( f(x) = x - [x] \) represents the fractional part of \( x \), which has discontinuities at integer values of \( x \).
Step 2: In the interval \( (0, 7) \), there are 6 integer points where the function will be discontinuous: \( x = 1, 2, 3, 4, 5, 6 \).

Final Answer: \[ \boxed{6} \]