Show that the modulusfunction `f: R->R`, given by `f(x)=|x|`is neither – InterviewSolution

1.	Show that the modulusfunction `f: R->R`, given by `f(x)=\|x\|`is neither one-one noronto.
Answer» We have `f(-1) =\|-1\| =1 " and " f(1) =\|1\| =1` Thus two different elements in R have the same image `:.` f is not one-one If we consider -1 in the codomain R then it is clear that there is no real number x whose modulus is -1 Thus -1 `in R ` has no pre- image in R `:. ` f is not onto. Hence f is neither one-one nor onto.

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