Question

Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√x−[x] is discontinuous is _____.

Answer 1

Correct Answer: 2

We need to check for discontinuity at doubtful points \( x \in I \).

At \( x = -1 \):

\( f(-1^+) = 1 + 0 = 1 \)

\( f(-1^-) = 2 + 1 = 3 \)

At \( x = 0 \):

\( f(0^+) = 0 + 0 = 0 \)

\( f(0^-) = 1 + 1 = 2 \)

At \( x = 1 \):

\( f(1^+) = 1 + 0 = 1 \)

\( f(1^-) = 0 + 1 = 1 \)

From the above calculations, discontinuity occurs at two points.