COMEDK · Maths · 24. Functions
If \(R\) denotes the set of all real number, then the function \(f: R \rightarrow R\) defined \(f(x)=|x|\) is
- A one-one only
- B onto only
- C both one-one and onto
- D neither one-one nor onto
Answer & Solution
Correct Answer
(D) neither one-one nor onto
Step-by-step Solution
Detailed explanation
We have, \[ \begin{array}{lrlrl} & & f(x) & =|x| \\ \text { Now, } & f(1) & =|1|=1 \\ \text { and } & f(-1) & =|-1|=1 \\ & \therefore & f(1) & =f(-1) \text { but } 1 \neq-1 \end{array} \] So, \(f(x)\) is not one-one. Again, \(|x| \geq 0, \forall x \in R\) So, range of…
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