Give an example (or prove that none exists) of a real function f(x) which is continuous, invertible,

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Give an example (or prove that none exists) of a real function f(x) which is continuous, invertible, and satisfies the following identity everywhere on its domain of definition: f^-1(x)=1/f(x)

Aug 3rd, 2015

Thank you for the opportunity to help you with your question!

For functions, the notations mean the same thing, but "f(x)" provides more flexibility and more information. You used to say "y=4x+ 3; solve for y when x = –1". Now you say f(x)= 4x + 3; find f(–1)" (pronounced as "f-of-x is 4x plus three; find f of negative one.

Do exactly the same thing for each: you plug in –1 for x. and *2, and then +3, simplifying to get a value of -1

In the question, f(x) will be contionous when the values of f^-1(x) will be equal to that of its reciprical.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 3rd, 2015

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Aug 3rd, 2015
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