Mathematics, 25.02.2020 05:55 gebradshaw2005
State whether each of the following functions f have a well-defined inverse or not. Recall that a function has an inverse if, for every element in the codomain, there exists exactly one element in the domain that maps to it; that is, the function is onto (surjective) and one-to-one (injective). If it does, provide the inverse function f β1 . If it does not, explain if it violates the onto condition, one-on-one condition, or both, and justify your response. (a) f : R β R, f(x) = 3xβ12 (b) f : R β R, f(x) = x 2 +1 (c) f : R β R, f(x) = 3x 3 β12x (d) f : R + β R +, f(x) = β x+1, where R + denotes the positive reals
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State whether each of the following functions f have a well-defined inverse or not. Recall that a fu...
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