What does [x] mean? The floor function?
As for (x/y)-xy=1, write it as xy^2+y-x=0 and use the quadratic equation for y.
Find the inverse of f(x)=x+[x].
Let g(x) be the inverse of f(x). I keep getting
g(x)={ x/2 if x is an integer
g(x)={ x-([x]/2) if x is not an integer
This works for g(f(x))=I(x)
but when I try f(g(x)),
f(g(x))={x if [x] is even and
f(g(x))={x-(1/2) if [x] is odd
Which is not the identity function (clearly)...
Also, I cannot figure out how to find the inverse of
h(x)=x/(1-(x^2)) for -1<x<1
If y is the inverse of h(x), I get (x/y)-xy=1 which reminds me of a circle or hyperbola or something but I cant rearrange it to make a recognizable formula...