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A certain function f (x) has the propert...

A certain function `f (x)` has the property that `f (2x)=alpha f (x)` for all positive real values of x and `f (x) =1- |x-2| ` for `1 le x le 3`
If the total area bounded by `y= f (x) and ` x-axis in `[1, oo)` converges to a finite quantity, then the range of `alpha` is:

A

`(-1, 1)`

B

`(-(1)/(2), (1)/(2))`

C

`(-(1)/(3), (1)/(3))`

D

`(-(1)/(4), (1)/(4))`

Text Solution

Verified by Experts

The correct Answer is:
C
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