Find all points of discontinuity of f, where`f(x)={{:((sinx)/x , ifx<0),(x+1, ifxgeq0):}`

Explanation

It is evident that f is defined at all point of the real line

Let c be a real number


Case 1

If `c<0` , then `f(c)=(sinc)/c` and `lim_(xrarrc)f(x)=lim_(xrarrc)(sinx)/x=(sinc)/c`

Therefore , f is cont. at all points x, such that `x<0`


Case 2

If 'c>0' , then 'f(c)=c+1' and `lim_(xrarrc)f(x)=lim_(xrarrc)(x+1)=c+1`

`:.lim_(xrarrc)f(x)=f(c)`

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