Home
Class 12
MATHS
Prove that the Greatest Integer Function...

Prove that the Greatest Integer Function `f : R->R ,`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

    MODERN PUBLICATION|Exercise NCERT - FILE (Question from NCERT Book) (Exercise 1.3)|15 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise NCERT - FILE (Question from NCERT Book) (Exercise 1.4)|13 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise NCERT - FILE (Question from NCERT Book) (Exercise 1.1)|16 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise MOCK TEST SECTION D|6 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

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

Solve the equation x^(3)-[x]=3 , where [x] denotes the greatest integer less than or equal to x .

The greatest integer function f:R rarr R given by f(x)=[x] is:

lim_(xrarr oo) (log[x])/(x) , where [x] denotes the greatest integer less than or equal to x, is

Show that f:R rarr R, given by f(x)=x-[x], is neither one-one nor onto.

Show that f:R rarr R, given by f(x)=x-[x], is neither one-one nor onto.

Show that f:R rarr R, given by f(x)=x-[x], is neither one-one nor onto.

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

The function f(x)=x-[x]+cos x, where [x]= the greatest integer less than or equal to x is a