It is given that f : R → R, given by f (x) = | x|
We can see that f(-1) = |-1| = 1, f(1) = |1| = 1
⇒ f(-1) = f(1), but -1 ≠ 1.
⇒ f is not one-one.
Now, we consider -1 ϵ R.
We know that f(x) = |x| is always positive
Therefore, there doesn't exist any element x in domain R such that f(x) = |x| = -1
⇒ f is not onto.
Therefore, modulus function is neither one-one nor onto.
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