Show that ƒ(x) = is continuous at each point except 0.

Question

Philoid · Accepted Answer

Given function is ƒ(x) =

Left hand limit at x = 0

= 0

Right hand limit at x = 0

= 0

Also,

f(0) = 1

As,

f(x) = x for other values of x expect 0 f(x) = 1,2,3,4…

Therefore,

f(x) is not continuous everywhere expect at x = 0