MHB Is f(x) Its Own Inverse for Any Value of a?

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The function f(x) = a + 4/(x-a) has been analyzed for its inverse properties. The derived inverse function f-1(x) = (a^2 - ax - 4)/(a - x) is deemed incorrect by some participants. Discussions revolve around whether f(x) is its own inverse for various values of a, with claims that it may only hold true for specific conditions. The consensus suggests that the function is not its own inverse universally. The investigation highlights the complexity of determining inverse relationships in this context.
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f(x)=a+4/(x-a)
f-1(x)=(a^2-ax-4)/(a-x)

Which of the following is true?
The function is the opposite of its own inverse for any value of a.
The function is its own inverse for positive values of a only.
The function is the reciprocal of its own inverse for positive values of a only.
The function is its own inverse for negative values of a only.
The function is its own inverse for any value of a.
 
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Re: Inverse functions problem help please

What has your investigation led you to find?
 
bcasted said:
f(x)=a+4/(x-a)
f-1(x)=(a^2-ax-4)/(a-x)

...

If this equation: $$f^{-1}(x)=\frac{a^2-ax-4}{a-x}$$
is meant to be the equation of the reverse function then this equation is false.
 

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