CUET · MATHS · PYQ PAPER 2025
Let \(f(x)=\left\{\begin{array}{ll}|x|+3 & \text { if } x \leq-3 \\ -2 x & \text { if }-3 < x < 3, \text { then which of the following is true? } \\ 6 x+2 & \text { if } x \geq 3\end{array}\right.\)
- A \(f(x)\) is discontinuous at both \(x=3\) and \(x=-3\)
- B \(f(x)\) is continuous at both \(x=3\) and \(x=-3\)
- C \(f(x)\) is discontinuous at \(x=-3\)
- D \(f(x)\) is discontinuous at \(x=3\)
Answer & Solution
Correct Answer
(D) \(f(x)\) is discontinuous at \(x=3\)
Step-by-step Solution
Detailed explanation
At \(x=-3\): \(f(-3) = |-3|+3 = 6\) \(\lim_{x \to -3^-} f(x) = |-3|+3 = 6\) \(\lim_{x \to -3^+} f(x) = -2(-3) = 6\) \(f(x)\) is continuous at \(x=-3\). At \(x=3\): \(f(3) = 6(3)+2 = 20\) \(\lim_{x \to 3^-} f(x) = -2(3) = -6\) \(\lim_{x \to 3^+} f(x) = 6(3)+2 = 20\)…
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