Functional Equation

[Sanguinne]

Another problem I need help with...

The function f satisfies the functional equation f(f(x))=x for the maximal domain of f. The rule for the function is

a) f(x) = x +1
b) f(x) = x - 1
c) f(x) = ( x - 1 )/( x + 1)
d) f(x) = ln(x)
e) f(x) =  ( x + 1 )/( x - 1)

[b^3]

Try each option and see.
So we are looking for , that is wherever you see , we are going to put back in the function, .

A

B

C

D

E

Which makes the answer E.

[Sanguinne]

thanks

i guess i was just making careless mistakes when simplifying

[fred42]

It should be noted that if (f(x)) = x, then the graph must be an inverse of itself and should therefore be symmetrical about the line y = x. This can help minimise the number of options that need to be checked.