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

[bcasted]

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.

 

[MarkFL]

Re: Inverse functions problem help please

What has your investigation led you to find?

 

[earboth]

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.