Parameter assumptions on utility functions

I wonder if the \alpha in Question 3(a) of Problem Set 4 is required to be between 0 and 1. If not, would it still be Cobb Douglas?
Also, could there be a condition on the \beta in 3(c) that \beta > 0 ? Otherwise it might not be a monotone increasing transformation of (a).
Both seem like eminently reasonable assumptions to me!
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