Answer 1

The given function f is  `f(x) = {(x^10 - 1, ","if x <= 1),(x^2, ","if x > 1):}`

The given function f is defined at all the points of the real line.

Let c be a point on the real line.

Case I:

Therefore, f is continuous at all points x, such that x > 1

Thus, from the above observation, it can be concluded that x = 1 is the only point of discontinuity of f.