If is a real-valued function discontinuous at all integral points lying in and if

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

f(x)

is a real-valued function discontinuous at all integral points lying in

[0, n]

and if

(f(x))^2 = 1, \forall x \in [0, n]

, then number of functions

f(x)

are (1)

2^{n+1}

(2)

6 \times 3^n

(3)

2 \times 3^{n-1}

(4)

3^{n+1}