QJEEM21Ma4e0e: JEE Main 2021 Mathematics - Class 12 JEEM21Ma4e0e Solution: Let f : R → R be defined as f ( x ) = { 2 sin ⁡ ( − π x 2 ) , i …

Question

Verified Solution • 2025–26 Session moderate

Let f : R

\to

R be defined as

f (x) = {\begin{matrix} 2 \sin (- \frac{π x}{2}), i f x < - 1 \\ | a x^{2} + x + b |, i f - 1 \leq x \leq 1 \\ \sin (π x), i f x > 1 \end{matrix}

If f(x) is continuous on R, then a + b equals :

Accepted Answer

f (- 1^{-}) = 2

f (- 1^{+}) = | a + b - 1 |

| a + b - 1 | = 2

... (i)

f (1^{-}) = | a + b + 1 |

f (1^{+}) = 0

| a + b + 1 | = 0 \Rightarrow a + b + 1 = 0

\Rightarrow a + b = - 1

.... (ii)

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