Functional

Puzzles

• distributedFind all f: R -> R, f not identically zero, such that (*) f( (x+y)/(x-y) ) = ( f(x)+f(y) )/( f(x)-f(y) ).
• half.iterateLet f(x) = (sqrt(2))^x for x > 0; then f^-1(x) = 2 ln(x)/ln(2). New, unsolved
• linearSuppose f is non-decreasing with f(x+y) = f(x) + f(y) + C for all real x, y.
• minus.xIdentify a real valued function f(x) which has the property for all real x that f(f(x)) = -x. New