Question

Let f(x) = (x - [x])/(1 + x - [x]) where [x] donotes the greatest integer less than or equal to x then the range of f is

(a) [0, 1]

(b) [0, 1/2)

(c) [0, 1)

(d) [0, 1/2]

Answer 1

The correct option (b) [0, 1/2)

Explanation:

If [x] is greatest integer then x – [x] = p/q

Where p and q are positive integers and p < q so p + p < p + q