CUET · MATHS · PYQ PAPER 2023
Let \(f(x)=\left\{\begin{array}{ll}2 x-1, & x<1 \\ 1, & x=1 \\ x^2, & x>1\end{array}\right.\) then at \(x=1\)
- A \(f(x)\) is continuous from left only
- B \(f(x)\) is continuous from right only
- C \(f(x)\) is continuous
- D \(f(x)\) has removable discontinuity
Answer & Solution
Correct Answer
(C) \(f(x)\) is continuous
Step-by-step Solution
Detailed explanation
\(\lim_{x \to 1^-} f(x) = \lim_{x \to 1^-} (2x-1) = 2(1)-1 = 1\) \(\lim_{x \to 1^+} f(x) = \lim_{x \to 1^+} (x^2) = (1)^2 = 1\) \(f(1) = 1\) Since \(\lim_{x \to 1^-} f(x) = \lim_{x \to 1^+} f(x) = f(1) = 1\), \(f(x)\) is continuous.
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