Let $ f: R \rightarrow R $ be defined as $ f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x1\end{array}\right. $ If $ f(x) $ is continuous on $ R $, then $ a+b $ equals [JEE Main 2021, 26 Feb (Shift 2)]

Question

Let $ f: R \rightarrow R $ be defined as $ f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \text { if } x<-1 \ \left|a x^{2}+x+b\right|, & \text { if }-1 \leq x \leq 1 \ \sin (\pi x) & \text { if } x>1\end{array}\right. $ If $ f(x) $ is continuous on $ R $, then $ a+b $ equals [JEE Main 2021, 26 Feb (Shift 2)]

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Let \( f: R \rightarrow R \) be defined as \( f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \…

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Let \( f: R \rightarrow R \) be defined as \( f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), &amp; \…

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Let \( f: R \rightarrow R \) be defined as \( f(x)=\left\{\begin{array}{cc}2 \sin \left(-\frac{\pi x}{2}\right), & \…