Suppose all you know about a function f is that f(ab)= f(a) + f(b), A(upsidedown) a, b greater than 0.

Find f(1).

Here's a picture of it. It's part c. Thanks.

http://pic90.picturetrail.com/VOL237.../389570493.jpg

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- Jul 12th 2010, 03:16 PMrowdy3Need help on proofs
Suppose all you know about a function f is that f(ab)= f(a) + f(b), A(upsidedown) a, b greater than 0.

Find f(1).

Here's a picture of it. It's part c. Thanks.

__http://pic90.picturetrail.com/VOL237.../389570493.jpg__ - Jul 12th 2010, 04:11 PMskeeter
- Jul 12th 2010, 06:52 PMrowdy3
1=1*1, so

f(1)=f(1*1)

f(1*1)+f(1)+f(1)

f(1)=2f(1)

therefore, f(1)=0

f(x^2) = f(x*x) = f(x)+f(x) = 2f(x)

let y = sqrt(x)

f(x) = f(y*y) = f(y) + f(y)

therefore f(y) = f(x)/2