Letf :R rarr R be a continous function g...

Let`f :R rarr R` be a continous function given by `f(x+y)=f(x)f(y) "for all" x, y in R. if int _(0)^(2) f(x) dx = alpha " then "int_(-2)^(2) f(x) dx` is equal to

A

`2 alpha`

B

`alpha`

C

0

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

C

We have,
`f(x+y)=f(x)+f(y)"for all" x, y in R`
`rArr f(x) = lambda, x "for all" x in R, "where" lambda= f(1)`
f(x() is an odd function.
`underset(-2)overset(2)int f(x)dx=0`

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