Find the relationship between ‘a’ and ‘b’ so that the function ‘f’ defined by is continuous at x = 3.

we have to find the value of 'a' & 'b'

Given:

f(x) is continuous at x = 3

If f(x) is be continuous at x = 3,then,f(3)^{–} _{=} f(3) ^{+} _{=} f(3)

LHL = f(3)^{–} _{=}

⇒ 3a – 0 × a + 1

⇒ 3a + 1 .....(1)

LHL = f(3) ^{+} =

⇒ 3b – 0 × b + 3

⇒ 3b + 3 ...(2)

Since ,f(x) is continuous at x = 3 and From (1) & (2),we get

3a + 1 = 3b + 3

⇒ 3a + 3b = 3 – 1

⇒ 3a + 3b = 2

⇒ 3(a + b) = 2

⇒ (a + b) =

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