6. Let f be a function such that f(xy)=xf(y)+yf(x) for all r, y E R. Prove that f(1) = 0 and that f(u") = nu-f(u) for al

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6 Let F Be A Function Such That F Xy Xf Y Yf X For All R Y E R Prove That F 1 0 And That F U Nu F U For Al 1 (12.7 KiB) Viewed 8 times

6. Let f be a function such that f(xy)=xf(y)+yf(x) for all r, y E R. Prove that f(1) = 0 and that f(u") = nu-f(u) for all u ER and n E N. Hint: What should you plug in to compute f(1)? Then how could you find f(u) if you already know f(u)? How would you then find f(u³)?