Question

Consider the function f : Z → Z defined by f(x) = x 2 . Is this function one-to-one, onto, or neither? Give justification for your claims that rely on definitions.

With explanation please

Answer 1

The given function is neirher one to one nor onto .

It is many one into

Because Z is the set of all integers positive and negative both

Clearly f(x) = x2 always gives non negative values that will be positive integers or 0 only and not negative integers making the function into

Also f(-1) = f(1) = 1 that means for two different x we have same value of y making the function many one .

Hence the given function is neither one one nor onto , rather it is many one into.