If function
`f(x)=x-(|x|)/(x),x lt 0`
`=x+(|x|)/(x),x gt 0`
`=1,x=0`, then

Answer

C

Explanation

Given function,
`f(x)=x-(|x|)/(x),x lt 0 = x+(|x|)/(x),x gt 0=1, x=0`
Now, at x=0
`LFL= underset(xto0^(-))(lim)f(x)=underset(xto0^(-))(lim)(x-(|x|)/(x))`
`underset(xto0)(lim)(x-((-x))/(x))=underset(xto0)(lim)(x+1)=1`
`RHL=underset(xto0^(+))(lim)" "f(x)=underset(xto0^(+))(lim)+(x+(|x|)/(x))`
`=underset(xto0)(lim)(x+1)=1 and f(0)=1`
`underset(xto0^(-))(lim)f(x)=underset(xto0^(+))(lim)f(x)=f(0)=1`
`impliesf(x)` is continuous at x=0.