A real function f is said to be continuous at x = c, where c is any point in the domain of f if

A function is continuous at x = c if

Function is changing its nature (or expression) at x = 2, so we need to check its continuity at x = 2 first.

=> LHL = RHL = f (2)

∴ Function is continuous at x = 2

Let c be any real number such that c > 2

∴ f (x) is continuous everywhere for x > 2.

Let m be any real number such that m < 2

∴ f (m) = 2m – 1 [using equation 1]

∴ f (x) is continuous everywhere for x < 2.

Hence, we can conclude by stating that f(x) is continuous for all Real numbers