Question

Q.6 Show that f(x) = (x) greatest integer function is neither 1-1 nor onto​

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.

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