CUET · MATHS · PYQ PAPER 2023
If the function \(f(x)=x^2\) is one-to-one and onto, then the domain D and range R of \(f(x)\) are respectively :
- A \(D=[-1,1], R=\) set of all real numbers
- B \(D=\) set of all real numbers, \(R=[0, \infty)\)
- C \(D=[0, \infty), R=\) set of all real numbers
- D \(D=[0, \infty), R=[0, \infty)\)
Answer & Solution
Correct Answer
(D) \(D=[0, \infty), R=[0, \infty)\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^2\) For \(f(x)\) to be one-to-one, restrict \(D=[0, \infty)\). For this domain, the range is \(R=[0, \infty)\). For \(f(x)\) to be onto, the codomain must be equal to its range. So, \(R=[0, \infty)\). Thus, \(D=[0, \infty), R=[0, \infty)\).
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