- #1

My Name is Earl

- 12

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Suppose that we have a function f(x) such that f(ab) = f(a)+f(b) for all rational numbers a and b.

(a) Show that f(1) = 0.

(b) Show that f(1/a) = -f(a).

(c) Show that f(a/b) = f(a) - f(b).

(d) Show that f(a

For (a), if ab = 1 then a = 1/b and b = 1/a. Not sure how to proceed from here.

(a) Show that f(1) = 0.

(b) Show that f(1/a) = -f(a).

(c) Show that f(a/b) = f(a) - f(b).

(d) Show that f(a

^{n}) = nf(a) for every positive integer a.For (a), if ab = 1 then a = 1/b and b = 1/a. Not sure how to proceed from here.

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