CUET · MATHS · PYQ PAPER 2023
If \(f: R \rightarrow A\) given by \(f(x)=x^2-6 x+12\) is a surjective function, then the set \(A\) is :
- A \((3, \infty)\)
- B \((-\infty, 3)\)
- C \([3, \infty)\)
- D \((-\infty, 3]\)
Answer & Solution
Correct Answer
(C) \([3, \infty)\)
Step-by-step Solution
Detailed explanation
\(x = -\frac{b}{2a} = -\frac{-6}{2(1)} = 3\) \(f(3) = (3)^2 - 6(3) + 12 = 9 - 18 + 12 = 3\) \(\text{Range}(f) = [3, \infty)\) \(A = [3, \infty)\)
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