Thread: Showing one to one

f(x) = 2x^3 - (cosx)^3, x for all [0, pi]. Show f is one to one and find (f^-1)'(-1). Note (0,-1) for all f.

x = 2y^3 - (cosy)^3

Is there a way I can factor the y so there is only one of them?

On observe that . That means that is increasing there.
Moreover, .