Question

Q11. Prove that the greatest integer function f: R R, given by f(x) = [x] is
neither one-one nor onto, where [x] denote the greatest integer function less
than or equal to x.​

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 than or equal to 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-one.

Step-by-step explanation:

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