Question

The number of points of discontinuities of f(x) = 2x² + [x²] – [x] where [.] is greatest integer function and x∈[–1, 2] is equals to___

Answer 1

Correct answer is : 4

f(x) = 2x² + [x²] – [x], x∈[–1, 2]

This function may be discontinuous at x = –1, 0, 1, √2 , √3 and √2.

For continuity at x = -1 

f(-1) = 4

\(\therefore\) f(x) is discontinuous at x = -1

For continuity at x = 0, f(0) = 0 

f(0^-) = 1 

\(\therefore\) f(x) is discontinuous at x = 0 

Continuity at x = 1

\(\therefore\) f(x) is continuous at x = 1

For continuity, at x = √2 and √3 similarly it is discontinuous 

For continuity at x = 2

f(2) = 2.2² + [2²] – [2] = 10

= 8 + 3 – 1 

= 10 

\(\therefore\) f(x) is continuous at x = 2

f(x) is discontinuous at x = -1, 0, √2 and √3 . 

No. of points of discontinuity = 4