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

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rnefyna1

Mathematics

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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)

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Explanation & Answer

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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.


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