Answer
f is not continuous on its domain.
discontinuity at x=1.
Work Step by Step
The function f is said to be continuous on its domain if it is continuous at each point in its domain. A discontinuity can occur at $x=a$ if either
a. $\displaystyle \lim_{\mathrm{x}\rightarrow a}f(x)$ does not exist, or
b. $\displaystyle \lim_{\mathrm{x}\rightarrow a}f(x)$ exists but is not equal to $f(a)$.
At endpoints of the domain (if any), we observe the existence of the left or right limit, as appropriate.
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At x=1, the left limit of f(x) is -1, as is the right limit.
The limit $\displaystyle \lim_{\mathrm{x}\rightarrow 0}f(x)$ does exist, and it is $-1$,
but it is not equal to $f(1)=1$.
We have found a discontinuity of type (b) at x=1.
f is not continuous on its domain
