Question:
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 ?
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 ?
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 ?
Updated On: Oct 1, 2024
- S has 13 elements
- S has 7 elements
- S is an infinite set
- S has 6 elements
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The Correct Option is D
Solution and Explanation
The correct option is (D) : S has 6 elements.
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