Refers to the functional domain.
2.f(x+ 1) is an even function. What is the symmetry axis of f(2x)? I think it's x= 1.
F(x+ 1) is an even function.
Let t=x+ 1.f(t) image be symmetric about t=- 1,
The f(x+ 1) image is symmetrical about x=- 1 (as shown in the figure, the red curve in the figure).
The symmetry axis of f(2x) is x=0. (as shown in the figure, the green curve in the figure).
3. A function f(x), x∈D, where d refers to the domain of the function itself or a domain in the domain of the function itself.
D here refers to the domain of the function itself.
4. If f(x+ 1) is odd function, is it -f(x+ 1) =f(-x- 1) or =f(-x+ 1)?
F(x+ 1) is odd function,
There is f[-(x+ 1)]=-f(x+ 1).
That is,-f (x+1) = f [-(x+1)] = f (-x-1).