Thread: Need 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

Originally Posted by rowdy3

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

so ... if , what must equal?

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