Question

if the function f:R --> A given by f(x)=[x]-x (where [.] denotes greatest integer function) is onto, then A is equal to
options
[0,1)
(-1,0]
R
(-1,1)

Answer 1

Answer:

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

f(x) = [x] It is seen that f(1.2) = [1.2] = 1, f(1.9) = [1.9] = 1 . f(1.2) = f(1.9) , but 1.2 ≠ 1.9 f is not one - oneNow, consider 0.7 ∈ R It is known