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Question: The function f(x) is discontinuous only at x = 0 such that f<sup>2</sup>(x) = 1 ∀ x ∈ R. Then, the t...

The function f(x) is discontinuous only at x = 0 such that f2(x) = 1 ∀ x ∈ R. Then, the total number of such functions is

A

2

B

3

C

6

D

None of these

Answer

6

Explanation

Solution

f(x) = f(x) = {1,x<0−1,x≥0\left\{ \begin{array} { c c } 1 , & \mathrm { x } < 0 \\ - 1 , & \mathrm { x } \geq 0 \end{array} \right.

f(x) = {−1,x≤01,x>0\left\{ \begin{array} { c c } - 1 , & \mathrm { x } \leq 0 \\ 1 , & \mathrm { x } > 0 \end{array} \right. f(x) =

f(x) = f(x) = {−1,x>0−1,x<01,x=0\left\{ \begin{array} { c c } - 1 , & x > 0 \\ - 1 , & x < 0 \\ 1 , & x = 0 \end{array} \right.