Let f: R->R be a continuous function and...

Let `f: R->R` be a continuous function and `f(x)=f(2x)` is true `AAx in R`. If `f(1)=3,` then the value of `int_(-1)^1f(f(x))dx` is equal to

A

3f(0)

B

0

C

3f(3)

D

6

Text Solution

Verified by Experts

The correct Answer is:

D

We have,
f(x)=f(2x) for all `x in R` and f(1)=3
`rArr f(x)=3` for all `x in R`
`rArr f(f(f(x)))=3` for all `x in R`
`rArr underset(-1)overset(1)int f(f(f(x)))dx=underset(-1)overset(1)int3dx=6`

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