Show that the signum function `f: R to R` defined by `f(x) ={ [-1 if x – InterviewSolution

1.	Show that the signum function `f: R to R` defined by `f(x) ={ [-1 if x lt 0], [0 if x=0], [1 if x gt 0]}` is neither one-one nor onto.
Answer» Clearly `f(2) =1 "and " f(3) =1` Thus `f(2) =f(3) " while " 2 ne 3` `:. ` f is not one-one Range `(f) ={1 ,0, -1} sub R.` So f is onto. Hence f is neither one-one nor onto.

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