what are all values of x such that 1x has a period of 1 exam

what are all values of x such that 1/x has a period of 1. (examples of possible values of x are 3 and (2^a * 5^b) )

Solution

Say f(x)=1/x

f(x) has period one so

f(x+1)=f(x)

1/(x+1)=1/x

x+1=x

From here we can\'t find the value of x for which x+1=x

So there is no value for which 1/x has period 1

In example given that x=3

But 1/3+1 =1/4 and this not same as 1/3 .so 1/3 doesn\'t have period 1.