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The function f(x) is discontinuous only ...

The function `f(x)` is discontinuous only at `x=0` such that `f^2(x)=1AAx in Rdot` The total number of such functions is `2` b. `3` c. `6` d. none of these

A

2

B

3

C

6

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
(i) `f(x)={{:(1",",xle0),(-1",",xgt0):}`
(ii) `f(x)={{:(1",",xlt0),(-1",",xge0):}`
(iii) `f(x)={{:(-1",",xle0),(1",",xgt0):}`
(iv) `f(x)={{:(-1",",xlt0),(1",",xge0):}`
(v) `f(x)={{:(1",",xgt0),(1",",xlt0),(-1,x=0):}`
(vi) `f(x)={{:(-1",",xgt0),(-1",",xlt0),(1,x=0):}`
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