Iat Iiser
Limits Continuity And Differentiability
IAT (IISER) 2026
MCQ+4 / -12026
For real numbers $a$ and $b$, consider the function $f : \mathbb{R} \rightarrow \mathbb{R}$ given by
$f(x) = \begin{cases} -ax - b & \text{if } x < -1, \\ 5x + 1 & \text{if } -1 \leq x \leq 1, \\ a^2x + 3b & \text{if } x > 1. \end{cases}$
How many pairs $(a, b)$ are there for which $f$ is continuous at every point of $\mathbb{R}$?
$f(x) = \begin{cases} -ax - b & \text{if } x < -1, \\ 5x + 1 & \text{if } -1 \leq x \leq 1, \\ a^2x + 3b & \text{if } x > 1. \end{cases}$
How many pairs $(a, b)$ are there for which $f$ is continuous at every point of $\mathbb{R}$?