I think since the group in the domain is additive so $$f(-8)=f[(-2)+(-2)+(-2)(-2)]=f(-2)f(-2)f(-2)f(-2)$${since $f$ is a homomorphism}. Hence $f(-8)= 5\cdot 5\cdot 5\cdot5=625.$ Is my explanation valid? Please suggest.
help me with verification of group homomorphism problem
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group-homomorphism
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1I think you are right. Since the domain is additive, $f\left(-2^3\right)=f[(-2)(-2)(-2)]$ is not $f(-2)f(-2)f(-2)$. – 2017-01-17