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Functions : Domain, Increasing/Decreasing, Image Set and Inverse

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This question concerns the function,f (x) = ln (x + 3).

a) State the domain of the function f, justifying your answer briefly.

b) State whether the function f is: increasing, decreasing, neither increasing nor decreasing, one-one or many-one.

c) Write down the image set of f.

d) Explain briefly why the function f has an inverse function f-1, and give the domain of f-1.

e) Find the rule of f-1, by first writing y = ln (x + 3) and solving this equation to find x in terms of y. (you should then write your answer in the form f-1 (x) = ..)

f) Write down the image set of f-1.

Please see attachment for proper citation of "f-1"

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Solution Summary

A function is investigated for its domain, regions of increase or decrease, image set and inverse.

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