Let S2(r) = {x ∈ R3 : |x| = r} for r > 0 and let f : S2 → S2(r) by f(x) = rx. Prove that f is one-to-one and onto but no

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answerhappygod
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Let S2(r) = {x ∈ R3 : |x| = r} for r > 0 and let f : S2 → S2(r) by f(x) = rx. Prove that f is one-to-one and onto but no

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Let S2(r) = {x ∈ R3 : |x| = r} for r >
0 and let f : S2 → S2(r) by f(x) = rx. Prove
that f is one-to-one and onto but not an isometry if r /= 1
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