Question

If ƒ(x) = $f(x) = x^{3} - x$, then the points of discontinuity of the function ƒ³ⁿ , (x) is/are where ƒⁿ = ƒoƒ….oƒ (n times), are –

• A. x = 2
• B. x = {0, 1}
• C. x = –1
• D. Continuous everywhere

Answer 1

Answer: (B)

x = {0, 1}

Answer 2

Clearly, x = 1 is a point of discontinuity of the function ƒ(x)

=.

If x ≠ 1, then (ƒoƒ) (x) = ƒ[ƒ(x)]

= ƒ = , which is discontinuous at x = 0.

If x ≠ 0 and x ≠ 1, then

(ƒoƒoƒ) (x) = ƒ[(ƒoƒ) (x)] = ƒ = x,

Which is continuous everywhere.

So, the only points of discontinuity are x = 0 and x = 1.

Hence (2) is the correct answer.