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Let f(x)={(0.1).3^[[x]]}. (where [.] den...

Let `f(x)={(0.1).3^[[x]]}`. (where [.] denotes greatest integer function and denotes fractional part). If `f(x + T) =f(x) AA x in 0`, where T is a fixed positive number then the least x value of T is

A

2

B

4

C

6

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x+4)={(0.1)3^([x+4])}`
`={(0.1)xx81xx3^([x])}`
`={8xx3^([x])+(0.1)3^([x])}`
`={(0.1)3^([x])}=f(x)`
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