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.
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                    Step  by step



<pre>
(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   = {{{root(3, 9-x)}}}.


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

        f^-1(x) = {{{root(3, 9-x)}}}.    <U>ANSWER</U>
</pre>

Done.


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



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;MEMORIZE &nbsp;IT &nbsp;(&nbsp;!&nbsp;)



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