CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=\left\{\begin{array}{cl}\frac{x^2+2 x-3}{x-1} & , x \neq 1 \\ 2 & , x=1\end{array}\right.\) is :
- A continuous at \(x =1\)
- B discontinuous at \(x =1\)
- C continuous at every real number
- D discontinuous at every real number
Answer & Solution
Correct Answer
(B) discontinuous at \(x =1\)
Step-by-step Solution
Detailed explanation
\(f(1) = 2\) \(\lim_{x \to 1} f(x) = \lim_{x \to 1} \frac{x^2+2x-3}{x-1}\) \(= \lim_{x \to 1} \frac{(x+3)(x-1)}{x-1}\) \(= \lim_{x \to 1} (x+3) = 1+3 = 4\) Since \(\lim_{x \to 1} f(x) \neq f(1)\) (\(4 \neq 2\)), the function is discontinuous at \(x=1\).
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