A real function f is said to be continuous at x = c, where c is any point in the domain of f if
h is a very small positive number. i.e. left hand limit as x → c (LHL) = right hand limit as x → c (RHL) = value of function at x = c.
A function is continuous at x = c if
From equation 1, f(x) is changing its expression at x = 2
Given, f (x) is continuous everywhere
4+2a + b = 8
∴ 2a + b = 4
∴ b = 4 – 2a …………… equation 2
Also from equation 1, it is clear that f(x) is also changing its expression at x = 4
Given, f (x) is continuous everywhere
∴ 8a + 5b = 14 ……………….Equation 3
Putting value of a from equation 2 to equation 3