SOLUTION: The one-to-one function f is defined below. f(x)=9-x^3 Find f^-1(x), where f^-1 is the inverse of f.

Question 1200606: The one-to-one function f is defined below.
f(x)=9-x^3
Find f^-1(x), where f^-1 is the inverse of f.
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.
The one-to-one function f is defined below.
f(x)=9-x^3
Find f^-1(x), where f^-1 is the inverse of f.
~~~~~~~~~~~~~~~~

Step by step

(1)  Write

        y = 9 - x^3.


(2)  Swap x and y in the equation

        x = 9 - y^3.


(3)  Express "y" from this equation

        y^3 = 9 - x

        y   = .


(4)  Stop at this point. You just got  the inverse function.  It is

        f^-1(x) = .    ANSWER

Done.

-----------------

This methodology (this algorithm) works for any analytical one-to-one function.

MEMORIZE IT ( ! )

It works in the same form in thousands other similar cases and problems.

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