Find all points of discontinuity of f, where f is defined by`f(x)={{:(x+1, ifxgeq1),(x^2+1, ifx<1):}`

Explanation

case 1 :When x=1

f(x) is continuous at x = 1

if L.H.L=R.H.L=f(1)

if `lim_(x->1^-)f(x)=lim_(x->1^+)f(x)=f
(1)`

L.H.L at x-> 1

`lim_(x->1^-)f(x)=lim_(h->0)f(1-h)`

=`lim_(h->0)((1-h)^2+1)`

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