If f x = 4 + a x − 4 − a x x , − 1 ≤ x 0 3 x + 2 x − 8 , 0 ≤ x ≤ 1 is continuous in [ − 1 , 1 ], then the value of a is

Question

If f x = 4 + a x − 4 − a x x , − 1 ≤ x 0 3 x + 2 x − 8 , 0 ≤ x ≤ 1 is continuous in [ − 1 , 1 ], then the value of a is, 1, - 1, 1 2, - 1 2

MARKS App · Accepted Answer

Given that f x is continuous in the interval [ - 1 , 1 ] , so, it will be continuous at x = 0 . Now f 0 + = - 1 4 f 0 - = lim x → 0 - ⁡ 2 a x x ( 4 + a x + 4 - a x ) (rationalizing) = lim x → 0 - ⁡ 2 a 4 = a 2 Now f 0 + = f ( 0 - ) ( ∵ f ( x ) is continuous at point 0) ⇒ a 2 = - 1 4 ⇒ a = - 1 2

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