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Question: If [⋅] denotes greatest integer function then f(x) = \(\left( \frac{1}{2} \right)^{x(x - 1)}\) is...

If [⋅] denotes greatest integer function then f(x) = (12)x(x−1)\left( \frac{1}{2} \right)^{x(x - 1)} is

A

Discontinuous at many points

B

Continuous at 12(1+1+4log⁡2x)\frac{1}{2}\left( 1 + \sqrt{1 + 4\log_{2}x} \right)

C

Discontinuous at 2

D

All of above

Answer

All of above

Explanation

Solution

[x] is discontinuous at all integers