Discuss the continuity of the function `f(x)={x ,\ \ \ x >0 1,\ \ \ x=0-x ,\ \ \ x<0` at the point `x=0` .

Explanation

Given: `f(x)={l}x, x>0 1, x=0 -x, x<0.`


`(` LHL at `x=0)=lim _{x rightarrow 0^{-}} f(x)=lim _{h rightarrow 0} f(0-h)=lim _{h rightarrow 0} f(-h)`


`lim _{h rightarrow 0}-(-h)=0`


`(` RHL at `x=0)=`


`lim _{x rightarrow 0^{+}} f(x)=lim _{h rightarrow 0} f(0+h)=lim _{h rightarrow 0} f(h)`


`lim _{h rightarrow 0}(h)=0`


And,


`f(0)=1`


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