NIMCET 2018 Question Paper with solutions

f (x) = x + |x|
= =
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 = $\underset{\mathit{x}\to 0^{-}}{\lim }$ f (x) = $\underset{\mathit{h}\to 0}{\lim }$ f (0 - h) = 0
RHL $\underset{\mathit{x}\to 0^{+}}{\lim }$ f (x) = $\underset{\mathit{h}\to 0}{\lim }$f (0 + h) = $\underset{\mathit{h}\to 0}{\lim }$ 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 ∊ (- ∞ , ∞)