CUET · MATHS · PYQ PAPER 2023
The function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+2 x-3}{x-1} & x \neq 1 \\ 2 & x=1\end{array}\right.\) is :
- A continuous at \(x=1\) only
- 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
\(f(1) = 2\) \(\lim_{x \to 1} f(x) = \lim_{x \to 1} \frac{(x-1)(x+3)}{x-1} = \lim_{x \to 1} (x+3) = 1+3 = 4\) \(\lim_{x \to 1} f(x) \neq f(1)\) as \(4 \neq 2\). The function is discontinuous at \(x=1\).
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