For a real number a, let Which of the following statements is/are true?

GATE · 2026 · CS · Set 2

For a real number a, let

Which of the following statements is/are true?

1. A.

   The value of I(a) is independent of the value of a

2. B.

   The value of I(a) can vary with the value of a

3. C.

   There exists 𝑎 ∈ (−∞, +∞) such that 𝐼(𝑎) is a positive real number

4. D.

   There exists 𝑎 ∈ (−∞, +∞) such that 𝐼(𝑎) is a negative real number

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