Home
Class 12
MATHS
Prove that the greatest integer function...

Prove that the greatest integer function `f: RR rarr RR`, given by `f(x)=[x]`, is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.3|14 Videos
  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.4|13 Videos
  • RELATIONS AND FUNCTIONS

    NCERT BANGLISH|Exercise EXERCISE 1.1|16 Videos
  • PROBABILITY

    NCERT BANGLISH|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos
  • VECTOR ALGEBRA

    NCERT BANGLISH|Exercise Miscellaneous Exercise on chapter 10|19 Videos

Similar Questions

Explore conceptually related problems

The greatest integer function f(x)=[x] is -

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

Show that the function f: R toR. defined as f (x) =x ^(2), is neither one-one nor onto.

Prove that the mapping f: RR rarr RR defined by , f(x)=x^(2)+1 for all x in RR is neither one-one nor onto.

Show that the function defined by g(x) = x-[x] is a discontinuous at all integral points. Here [x] denotes the greatest integer less than or equal to x.

Let f(x) = (x^2-9x+20)/(x-[x]) where [x] denotes greatest integer less than or equal to x ), then

Show that the modulus function f: RR rarr RR , given by f(x)=|x| is neither one-one nor onto Where |x|={(x " when "x ge 0),(-x " when " x lt 0):}

Find all the points of discontinuity of the greatest interger function defined by f(x)= [x] , where [x] denote the greatest integer less than or equal to x.

Prove that, the function f: RR rarr RR defined by f(x)=x^(3)+3x is bijective .

If f(x)= [sin^2x] (where [.] denotes the greatest integer function ) then :