Thread: Urgent Test Help

so there are two problems on my pre-calc test that carries over into tomorrow. One of them:

If the function f(f(x)) = X represents every x for the domain, what will it's symmetry be? It's function?

It's a ridiculously vague question and I don't even know where to begin.

The second one:
If the domain and range of a function are (a, b) and (c,d) and a < b and c < d,

what is the domain and range of the function f(x) = k (-1/3x) - 1

Any ideas???

If f(f(x)) = x then you can say that if y = f(x) then x = f(y). So if the point (x,y) is on the graph of the function, then so is the point (y,x). The graph has x <-> y as a symmetry.

For the second, you're bieng asked what the inverse of the transformation x -> (-1/3x) does to the interval (a,b) and what the transformation y -> y-1 does to the interval (c,d).