ID: Class: 12 Subject: Math Topic: Continuity and Differentiability Type: Mcq Year: 2025

Question:

If \( f(x) = \begin{cases} 1, & \text{if } x \leq 3 \\ ax + b, & \text{if } 3 < x < 5 \\ 7, & \text{if } x \geq 5 \end{cases} \) is continuous for all real numbers, then find the values of \(a\) and \(b\):
  • A. \(a=3\), \(b=-8\)
  • B. \(a=3\), \(b=8\)
  • C. \(a=-3\), \(b=-8\)
  • D. \(a=-3\), \(b=8\)