Question

Given the function f(x) = 1 /(1 – x), the points of discontinuity of the composite function y = f3n (x), where fn (x) = fof …. of (n times) are (n ∈ N)

(A) 0, 1

(B) 2n

(C) 3n

(D) 2n + 1

Answer 1

Correct Option (A) 0, 1

Explanation:

The point x = 1 is a discontinuity of the function f(x) = 1/(1 – x). If x ≠ 1, then

u(x) = f(f(x)) = x −1/x .

Hence x = 0 is a point of discontinuity of the function u. If x ≠ 0, and x ≠ 1, then fofof(x) = x. Hence y = f3n(x) = (f3 (x)n) = x is continuous everywhere. Therefore, 0 and 1 are the only points of discontinuities of y.