JEE Mains · Maths · STD 12 - 5. continuity and differentiation
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 ..... .
- A \(-3\)
- B \(-1\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(-1\)
Step-by-step Solution
Detailed explanation
\(f( x )\) is continuous on \(R\) \(\Rightarrow f\left(1^{-}\right)=f(1)=f\left(1^{+}\right)\) \(|a+1+b|=\lim _{x \rightarrow 1} \sin (\pi x)\) \(|a+1+b|=0 \Rightarrow a+b=-1 ....(1)\) \(\Rightarrow\) Also \(f\left(-1^{-}\right)=f(-1)=f\left(-1^{+}\right)\)…
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