Find the values of a and b such that the function defined by

is a continuous function.

Given: is a continuous function

To find: value of a and b

Formula used:

f(x) is continuous at x = c where c is any real number

if L.H.L = R.H.L = f(c)

Since, f(x) is continuous at x = 2

So,

2a + b = 5

⇒ b = 5 – 2a………………………(1)

Since, f(x) is continuous at x = 10

So,

10a + b = 21

From (1):

⇒ 10a + 5 – 2a = 21

⇒ 8a = 21 – 5

⇒ 8a = 16

⇒ a = 2

Put this value of a in (1):

b = 5 – 2a

⇒ b = 5 – 2(2)

⇒ b = 5 – 4

⇒ b = 1

Hence, the value of a and b are 2 and 1 respectively