Show that the given function is one-to-one and find its inverse. etc

label Mathematics
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Oct 2nd, 2015

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

A function is one to one if it's inverse is a function:

To find the inverse we switch x and y and solve for y:

x = 10 - cuberoot(y+5)

cuberoot(y+5) = 10 - x

Cube both sides to get:

y+5 = (10 - x)^3

y = (10 - x)^3 - 5

So, the inverse function f^-1(x) = (10 - x)^3 - 5

You can easily verify that this a function with your graphing calculator

The range of the original function is all real numbers which is also true for the domain of the inverse function.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 2nd, 2015

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