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Show that the Modulus Function f : R->R ...

Show that the Modulus Function `f : R->R ,`given by `f (x) = | x |`, is neither one-one nor onto, where `| x |`is x, if x is positive or 0 and `| x |`is ` x`, if x is negative.

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`f: R to R and f(x) = |x|`
Let `x, y in R`
and` " " f(x) = f(y)`
`rArr " " |x| = |y|`
`rArr " " x = pm y`
`therefore f` is not one-one.
Again `-1 in R` and there does not exist `x in R` for which `f(x)=-1`
`therefore f ` is not onto.
Therefore, `f` is neither one-one nor onto.
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