help me to solve this problem please this is my soultion but i am not sure if it is correct
2026-02-23 06:16:21.1771827381
algebra problem - homomorphism
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The proof of a is perfect. The proof of b is not wrong but is too long and unnecessarily repeats the inductive argument. When you get to $\frac{1}{f(a^k)}$ just use part a of the problem to simplify (you can do this because $k$ is positive) and you are done!