^ Very helpful, thanks a lot. What exactly does well-defined mean? I think I have some idea of what it means but it's not concrete for me
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Other questions
1) In the Essential book, it says for the composition of g with f to be defined, the range of has to be a proper subset of the domain of g. Does this mean that the range has to be a subset of the domain of g but it can't EQUAL the domain of g?
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2) Let a be a positive number, let f: [2, infinity) -> R, f(x) = a-x and g: (-infinity, 1] -> R, g(x) = x^2+a. Find all values of a for which f o g and g o f both exist.
I got the correct answer but not after three tries and I'm looking for a more systemic way of doing it. The way I did it involved a bit of guessing and plugging in different numbers to check.
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3) For f: (-infinity, 2] -> R, f(x) = (x-2)^2
To find the inverse, how do you know to take the negative square root? Is the only way to tell just to look at the domain of f and hopefully realise that it must be the negative root to have as its range?
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4) Why is the horizontal translation in y=2^(-x+2) two units to the right and not left?