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Question

Let f(x) be a function in [0,5] such that f2(x)=1x[0,5] and f(x) is discontinuous at all integers in [0,5]. Find total number of fuctions.

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Solution

Asf2(x)=1;f(x)=1or1f:[0,5]{1,1}f(x)isdiscontinuousatallintegersin[0,5]f(0)=1,f(0+)=1,f(1)=1,......Nowateachintegerwehavetwooptions6times2=12Also,wecanhavef(0)=1andsoonSo,12×2=24functions

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