f:(-1,0)U(0,-1)→ R defined by f(x)= -1 ,if x <0 and f(x)=1 , if x>0 . Find f is continuous or not?

Question

I know that

lim f(x)=-1 ( where x tends to 0-)

and

lim f(x)=1,( where x tends to 0+) ,

so f should be discontinuous, am i right?

But in the book this is given that f is continuous. Explain how this happened ?

Answer 1

f(x) if defined in two intervals (0 to -1) and (-1 to zero)) which is equivalent to (0 to -1)

for x<0 ,,, f(x)=-1

f(x) is continuous in its defined interval.