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Find All Points of Discontinuity Of F, Where F Is Defined by F(X) = {(X^10 - 1, If X <= 1),(X^2, If X > 1) - Mathematics

Find all points of discontinuity of f, where f is defined by `f(x) = {(x^10 - 1, ","if x <= 1),(x^2, ","if x > 1):}`

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Solution

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.

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APPEARS IN

NCERT Class 12 Maths
Chapter 5 Continuity and Differentiability
Q 12 | Page 159
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