Discuss the continuity of the function `f(x)={{:(2x-1,ifx<2),((3x)/2 ,ifxgeq2):}`

Explanation

Given function
`f(x)={{:(2x-1,ifx<2),((3x)/2
,ifxgeq2):}`at the point `x=2`
LHL at `x=2`,
`lim_(x->2^-)f(x)`
`lim_(h->0)f(2-h)`
`=lim_(h->0)2(2-h)-1`
`=3`
RHL at `x=2`,
`lim_(x->2^+)f(x)`
`lim_(h->0)f(2+h)`
`=lim_(h->0)(3(2+h))/2`
`=6/2`
`=3`
Also,
`f(2)=(3xx2)/2=3`
here, `LHL = RHL =FV`
therefore this function is continuous at `x=2`