math

Question

someone plz give solution

Answer 1

I suppose u know a little about greatest integer function.(also known floor)

e.g. gof(2.00001) = gof(2.999999) = 2 only 

    gof(1.99999...) = 1 only .Keeping this in mind we have,

Hence the assertion that the function is discontinuous at x = 1 is valid as well as the reason provided that left hand limit of f(x) ≠ right hand limit of f(x) at x = 1.

In fact this function is a function representing fractional part of any number which is discontinuous hence at every integral points.From graph u can also verify that it is discontinuous at every integral points.