Question
Real Analysis Question on Functions of One Real Variable
For x ∈ ℝ, let ⌊x⌋ denote the greatest integer less than or equal to x.
For x, y ∈ ℝ, define
\min\left\\{x,y\right\\} = \begin{cases} x & \text{if } x \le y, \\\ y & \text{otherwise.} \end{cases}
Let f:[−2𝜋, 2𝜋] → ℝ be defined by
f(x) = sin(min{x, x − ⌊x⌋}) for x ∈ [−2𝜋, 2𝜋].
Consider the set S = {x ∈ [−2𝜋, 2𝜋]: f is discontinuous at x}.
Which one of the following statements is TRUE ?
A
S has 13 elements
B
S has 7 elements
C
S is an infinite set
D
S has 6 elements
Answer
S has 6 elements
Explanation
Solution
The correct option is (D) : S has 6 elements.