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If R denotes the set of all real number, then the function f: R R defined f(x)=|x| is

Options

  1. Aone-one only
  2. Bonto only
  3. Cboth one-one and onto
  4. Dneither one-one nor onto

Correct answer

D. neither one-one nor onto

Step-by-step solution

We have, array lrlrl & & f(x) & =|x| Now, & f(1) & =|1|=1 and & f(-1) & =|-1|=1 & & f(1) & =f(-1) but 1 -1 array So, f(x) is not one-one. Again, |x| 0, x R So, range of f(x)=[0, ] Range Co-domain So, f(x) is not onto.

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