CUET · MATHS · PYQ PAPER 2023
The function f defined by \((x)=\left\{\begin{array}{ll}a x+1, & x \leq 3 \\ b x+3, & x>3\end{array}\right.\) is continuous at x = 3 if
- A \(a=b-\frac{2}{3}\)
- B \(a=b+\frac{2}{3}\)
- C \(a=b-\frac{1}{3}\)
- D \(a=b+\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(a=b+\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
\( \lim_{x \to 3^-} f(x) = \lim_{x \to 3^+} f(x) \) \( a(3)+1 = b(3)+3 \) \( 3a+1 = 3b+3 \) \( 3a = 3b+2 \) \( a = b+\frac{2}{3} \)
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