# Find the values of a and b so that the function f given by is continuous at x = 3 and x = 5

Given:

f(x) is continuous at x = 3 & x = 5

If f(x) to be continuous at x = 3,then,f(3) = f(3) + = f(3)

LHL = f(3) = = 1 ...(1)

RHL = f(3) + =  a(3 + 0) + b

3a + b ...(2)

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

3a + b = 1 ...(3)

Similarly ,f(x) is continuous at x = 5

If f(x) to be continuous at x = 5,then, f(5) = f(5) + = f(5)

LHL = f(5) =  a(5–0) + b

5a + b ...(4)

RHL = f(5) + =  7 ...(5)

Since , f(x) is continuous at x = 5 and From (4) & (5),we get,

5a + b = 7 ...(6)

Now equate (3) & (6) a = 3

Now Substitute a = 3 in any one of above equation(3) & (6) ,

3a + b = 1

3(3) + b = 1

9 + b = 1

b = –8

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