Here, we see that f (x) is a polynomial functions, so it is continuous for every value of x except 0. Now, we have to check the continuity only at x = 0 LHL =
lim
x→0−
f (x) =
lim
h→0
f (0 - h) = 0 RHL
lim
x→0+
f (x) =
lim
h→0
f (0 + h) =
lim
h→0
2 (0 + ) = 0 and f (0) = 0 ∴ LHL = RHL = f (0) So, f (x) is continuous at x = 0 also Hence, f (x) is continuous at x ∊ (- ∞ , ∞)