If f x is continuous at x = 3 where f ( x ) = { a x + 1 , f o r x ≤ 3 b x + 3 , f o r x 3 , then

Question

If f x is continuous at x = 3 where f ( x ) = { a x + 1 , f o r x ≤ 3 b x + 3 , f o r x > 3 , then, a + b = - 2 3, a - b = - 2 3, a - b = 2 3, a + b = 2 3

MARKS App · Accepted Answer

We have, f x is continuous at x = 3 Where f x = a x + 1 f o r x ≤ 3 b x + 3 f o r x > 3 ∴ l i m x → 3 - f x = l i m x → 3 + f x = f 3 … i Now, l i m x → 3 - f x = l i m h → 0 f 3 - h = l i m h → 0 f 3 - h + 1 = 3 a + 1 … i i l i m x → 3 + f x = l i m h → 0 f 3 - h = l i m h → 0 b 3 + h + 3 = 3 b + 3 … (iii) and f 3 = 3 a + 1 … (iv) Since, f x is continuous at x = 3 ∴ From Eqs. (i), (ii), (iii) and (iv) we get 3 a + 1 = 3 b + 3 ⇒ 3 a - 3 b = 2 ⇒ a - b = 2 3

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