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

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

Grade:12

1 Answers

Harsh davda
41 Points
7 years ago
you see that.... for many values of x, u would get the same value of y... for eg. , put x=0.2 or 0.39 or 0.71... u would get the same value of y... hence the function is many-one. not one-one.. morever out of all the real numbers we get only integers as output.. hence all the values are not being covered from the range.. thus the function is into and not onto.. thanx.

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