Login/Sign Up
Home » Show that the function defined by is discontinuous at all integral points. Here denotes the greatest integer less than or equal to
Show that the function defined by g(x)=x-[x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x
CBSE | Class 12 | Continuity and Differentiability | Exercise 5.1 | Maths | NCERT
Show that the function defined by g(x)=x-[x] is discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x

Solution: Here, for any real number, x,

The fractional part or decimal part of x is denoted by [x].

For example let us consider,

[2.35]=0.35

[2]=0

[-5]=0

The function g: R->R defined by g(x)=x-[x] \forall x \in \infty is called the fractional part function.

The domain of the fractional part function is the set \mathrm{R} of all real numbers, and [0,1) is the range of the set.

As a result, given function is discontinuous function.

i

More Material