Prove that Zn Zn is notisomorphic to any subgroup of Zm for any m.
1 answer:
Answer and Step-by-step explanation:
Every group homomorphism ϕ:Zn→Zm extends in a unique way to a linear transformation T:Qn→Qm of vector spaces over Q.
Moreover, ϕ is injective iff T is injective. But T being injective implies n≤m.
Applying this to both ϕ and ϕ−1, we conclude that n≤m≤n.
NOTE:
The proof and step-by-step explanation is in the attachment below
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Answer:
{4}
Step-by-step explanation:
It is helpful to let a calculator or spreadsheet perform the function evaluations for you. The two functions have the same value only for x=4 in the domain.
f(4) = 13 = g(4)
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The functions also have the same value for x=-2, but that is not in the domain given.
