z=F(f(x)) double function?

Question

what's the name of this function?

Answer 1

I understand this to be a composite function.

 

z = F[f(x)]

 

f(x)=x+2y
F(x)=cosx

 

therefore z = F[f(x)] = F(x+2y) = cos(x+2y)

Answer 2

I can't be sure, but in some books,  the capital F denotes the Fourier transform of its argument.

If that is the case here,    z would be the Fourier transform of the function f(x).

In this case z would be a function of a frequency argument:  z =  z(f).