has a discontinuity of the first kind at x = 0
In case exists but is not equal to f(c) then the function is said to have a removable discontinuity. In this case we can redefine the function such that = f(c) & make it continuous at x = c.
In case does not exist then it is not possible to make the function continuous by redefining it . Such discontinuities are known as non  removable discontinuity.
In all these cases the value of f(a) of the function at x= a (point of discontinuity) may or may not exist but does not exist.
Remark
(i) In case of finite discontinuity the nonnegative difference between the value of the RHL at x = c & LHL at x = c is called The Jump Of Discontinuity . A function having a finite number of jumps in a given interval I is called a Piecewise Continuous or Sectionally Continuous function in this interval.
(ii) All Polynomials, Trigonometrical functions, Exponential & Logarithmic functions are continuous in their domains.
(iii) Point functions are to be treated as discontinuous is not continuous at x = 1.
(iv) If f is continuous at x = c & g is continuous at x = f(c) then the composite g[f(x)] is continuous at x = c.
are continuous at x = 0 , hence the composite will also be continuous at x = 0.
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1. What is a removable discontinuity? 
2. What is an irremovable discontinuity? 
3. How can you classify discontinuities? 
4. Can a function have both removable and irremovable discontinuities? 
5. How do discontinuities affect the behavior of a function? 

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