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The modulus function f: R->R , given b...

The modulus function `f: R->R` , given by `f(x)=|x|` is

A

One One

B

Many One

C

cant say

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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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