Let f:R to R be continuous function such...

Let `f:R to R` be continuous function such that f(x)=f(2x) for all `x in R`. If f(t)=3, then the value of `int_(-1)^(1) f(f(x))dx`, is

3f(0)

3f(3)

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The correct Answer is:

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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