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Q.

The function ⨍ (x) is discontinuous only at x=0 such that ⨍ 2(x)=1∀x∈R, ∀x∈R. Then the total number of such function is

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answer is 6.

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Detailed Solution

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fx=1x0-1x>0            fx=-1x01x>0 fx=1x<0-1x0             fx=-1x<01x0  fx=1x>0-1x=0     1x<0           fx=-1x>0-1x<01x=0 

There are six functions

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The function ⨍ (x) is discontinuous only at x=0 such that ⨍ 2(x)=1∀x∈R, ∀x∈R. Then the total number of such function is