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Shanghai Senior Three Mathematics Sanmao 20 16
1 and y=f(x) are increasing function defined on R+. Is R+ a domain or a range?

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).