lopez5628

25.02.2020 • 

Mathematics

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 −1 . If it does not, explain if it violates the onto condition, one-on-one condition, or both, and justify your response. (a) f : R → R, f(x) = 3x−12 (b) f : R → R, f(x) = x 2 +1 (c) f : R → R, f(x) = 3x 3 −12x (d) f : R + → R +, f(x) = √ x+1, where R + denotes the positive reals

Ответ:

3peak101

13.02.2020

Mathematics

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B) Square

A rectangle works as well, and it is the more general answer. If you were to rotate either figure along an axis parallel to one of the sides, then you will effectively create a revolving door motion. This sweeps out the 3D shape of a cylinder.

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