CUET · MATHS · PYQ PAPER 2025
The range of the function \(f(x)=4 x^2+12 x+7, x \in R\) is
- A \([-2, \infty)\)
- B \([0, \infty)\)
- C R
- D \((-2, \infty)\)
Answer & Solution
Correct Answer
(A) \([-2, \infty)\)
Step-by-step Solution
Detailed explanation
\(x_{vertex} = -\frac{12}{2(4)} = -\frac{3}{2}\) \(f(-\frac{3}{2}) = 4(-\frac{3}{2})^2 + 12(-\frac{3}{2}) + 7 = 4(\frac{9}{4}) - 18 + 7 = 9 - 18 + 7 = -2\) Range: \([-2, \infty)\)
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