Find the relationship between 'a' and 'b' so that the function 'f… - Vidyadip

Question

Find the relationship between 'a' and 'b' so that the function 'f' defined by:
$\text{f(x)}=\begin{cases}\text{ax + 1,} &\text{if x}\leq3\\\text{bx + 3,} & \text{if x > 3}\end{cases}\text{is continuous at x = 3.} $

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Answer

L.H.L. = 3a + 1
f (3) = 3a + 1
RHL = 3b + 3
since f(x) is continuous at x = 3, $\therefore$ 3a + 1 = 3b + 3.
OR 3a – 3b = 2, which is the required relation.

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