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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
(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.
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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.
