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While I was studying Calculus I saw an excercise like this:

The domain of f(x) [0,2] and the range is [0,1], it also shows its graphic, though it is not important it is something like a parabola, its maximum point is (1,1) and its intersection points are (0,0) and (0,2).

It asks me to show domains and ranges of some other functions. And one of them is that:

f(x+1)

It is just this, it doesn't write it like y=f(x+1) but I assume it.

Then the answer is that in solution appendix. Domain: [-1,1] and Range: [0,1]

I would be ok with it if it wrote Domain: x=[-1,1]. However if it asks the domain of the function, isn't it still the same function "f"? Shouldn't it have the same domain for its argument?

It may sound like a very small detail or useless but I really wonder your opinions.