If f x = x 2 + α for x ≥ 0 = 2 x 2 + 1 + β for x 0 is continuous at x = 0 and f 1 2 = 2 then α 2 + β 2 is

Question

If f x = x 2 + α for x ≥ 0 = 2 x 2 + 1 + β for x 0 is continuous at x = 0 and f 1 2 = 2 then α 2 + β 2 is, 3, 8 25, 25 8, 1 3

MARKS App · Accepted Answer

lim x → 0 + x 2 + α = lim x → 0 - 2 x 2 + 1 + β α = 2 + β ......... ( 1 ) f ( x ) = x 2 + α ; x ≥ 0 f ( 1 2 ) = 1 4 + α 2 = 1 4 + α 7 4 = α 7 4 − 2 = β ⇒ β = - 1 4 Hence α 2 + β 2 = 49 16 + 1 16 = 50 16 = 25 8

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