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Find all points of discontinuity of f, w...

Find all points of discontinuity of f, where f is defined by `f(x)={2x+3, if""""xlt=2`
`2x-3, if""""x >2`

Text Solution

Verified by Experts

Given
`f(x)={2x+3,if x<=2`
and `2x-3,if x>2}`
At`x=2 ` ,L.H.L`=lim_(x->2^(-))f(x)= lim_(x->2^(-))(2x+3)`
=` lim_(h->0)(2(2-h)+3)=7`
At`x=2 ` ,R.H.L`=lim_(x->2^(+))f(x)= lim_(x->2^(+))(2x-3)`
=` lim_(h->0)(2(2+h)-3)=1`
As,`L.H.L!=R.H.L`
...
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