JEE Main 2021 (Online) 26th February Evening ShiftQuestion 1
Let $f:\mathbf{R}\to\mathbf{R}$ be defined as
$f(x)=\begin{cases}2\sin\left(-\frac{\pi x}{2}\right), & \text{if } x<-1\\ \left|ax^{2}+x+b\right|, & \text{if } -1\le x\le1\\ \sin(\pi x), & \text{if } x>1\end{cases}$
If $f(x)$ is continuous on $\mathbf{R}$, then $a+b$ equals :
Limits & Continuity
Solution
At $x=1$: $|a+1+b|=\sin\pi=0\Rightarrow a+b=-1$. Check at $x=-1$: left value $2\sin\frac\pi2=2$, middle $|a-1+b|=|-2|=2$. Consistent. $a+b=-1$: option B.