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

Explanation

Given function
`f(x)=`
`{x, x>0`
`1, x=0`
`-x , x<0`
at the point `x=0`
LHL at `x=0`,
`lim_(x->0^-)f(x)`
`=lim_(h->0)f(0-h)`
`=lim_(h->0)f(-h)`
`=lim_(h->0)-(-h)`
`=lim_(h->0)h`
`=0`
RHL at `x=0`,
`lim_(x->0^+)f(x)`
`=lim_(h->0)f(0+h)`
`=lim_(h->0)f(h)`
`=lim_(h->0)h`
`=0`
also `f(0)=1`
here, `LHL=RHL ne functional value`
therefore this function is discontinuous at `x=0`