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Let f : R R; f(x) = 13 +x Let g: (0, oo)R: g(x)log3 a) What is the domain and codomain of f? b) What
Let f : R R; f(x) = 13 +x Let g: (0, oo)R: g(x)log3 a) What is the domain and codomain of f? b) What is the domain and codomain of g? c) Is f one-to-one? If not, show two elements of the domain which map to the same element of the codomain. d) Is f onto? If not, show an element of the codomain which isn't mapped onto by any element of the domain e) Is g one-to-one? If not, show two elements of the domain which map to the same element of the codomain. f) Is g onto? If not, show an element of the codomain which isn't mapped onto by any element of the domain. g) Is the inverse function f defined? If so, what is f-1(2)? If not, why not? h) Is the inverse function g defined? If so, what is g(2)? If not, why not? i) Is the composition f o g defined? If so, what is (f og)(2)? If not, why not? j) Is the composition g o f defined? If so, what is (g of) (2)? If not, why not
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