Question: Explain the continuity of the function f = |x| at x = 0.
Solution:
From the given function, we define that,
f(x) = {-x, if x<0 and x, if x≥0
It is clearly mentioned that the function is defined at 0 and f(0) = 0. Then the left-hand limit of f at 0 is
Limx→0- f(x)= limx→0- (-x) = 0
Similarly for the right hand side,
Limx→0+ f(x)= limx→0+ (x) = 0
Therefore, for the both left hand and the right hand limit, the value of the function coincide at the point x = 0.
Therefore, the function f is continuous at the point x =0.
