f (x) = x + |x| = {x+xx−xx≥0x<0 = {2x0x≥0x<0 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 = x→0−lim f (x) = h→0lim f (0 - h) = 0 RHL x→0+lim f (x) = h→0limf (0 + h) = h→0lim 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 ∊ (- ∞ , ∞)