How can I find f⁻¹. the inverse of f?

timer Asked: Oct 31st, 2015
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Question Description

The one-to-one function f is defined here:   f (x) = x³ -3

Find f⁻¹. the inverse of f

Then give the domain of f⁻¹ using interval notation

Tutor Answer

School: Rice University

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

If y = x^3 - 3

then the inverse function is x = y^3 - 3

y^3 = x + 3

y = (x+3)^(1/3) (i.e. y = cubic root of (x+3))

The range of f(x) = the domain of f^-1(x)

As the range of f(x) = ]-infinity,infinty[, that is the domain of the inverse function

Please let me know if you need any clarification. I'm always happy to answer your questions.

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Thanks, good work

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