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Let f(x) = x(2-x), 0 le x le 2. If the ...

Let `f(x) = x(2-x), 0 le x le 2`. If the definition of `f(x)` is extended over the set `R-[0,2]` by `f (x+1)= f(x)`, then f is a

A

periodic function with period 1

B

non-periodic function

C

periodic function with period 2

D

periodic function with period `1//2`

Text Solution

Verified by Experts

The correct Answer is:
C
For any `x in R -[0,2]` we have
`f(x+2) = f((x+ 1)+1)`
`rArr f(x+2) = f(x+1)" "[because f(x+1) = f(x)]`
`rArr f(x+2) = f(x+1) " "[because f(x+1) = f(x)]`
Therefore `f(x)` is periodic with period 2.
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