Let g(x) = 1 + x - [x] and f(x) = -1 for x 0, where [.] is the greatest integer function. For all real x, f(g(x)) equals:

Question

Let g(x) = 1 + x - [x] and f(x) = -1 for x < 0, 0 for x = 0, 1 for x > 0, where [.] is the greatest integer function. For all real x, f(g(x)) equals:

Accepted Answer

1. x - [x] = {x} is the fractional part, with 0 <= {x} < 1. Thus g(x) = 1 + {x} satisfies 1 <= g(x) < 2, which is always positive. Since f returns 1 for any positive argument, f(g(x)) = 1 for all x.

Let g(x) = 1 + x - [x] and f(x) = -1 for x < 0, 0 for x = 0, 1 for x > 0, where [.] is the greatest integer function. For all real x, f(g(x)) equals:

Solution

Related JEE Main Maths questions