- #1
Danijel
- 43
- 1
So, I'm a bit confused. The thing is, basically, all elementary functions are of the form ƒ:ℝ→ℝ. So the domain is ℝ and so is the codomain. However, if we have a function ƒ:ℝ→ℝ, given with f(x) = √x, it's domain is now x≥0. So, is the domain of this function ℝ or [0,+∞>?
Also, let's say we have two functions ƒ, and g, with f:A→B and g:C→D. Let's say that the image of the function f is f(A) ⊆ C. That way, we made sure that gof is defined. So, do we write gof: A → D, that is, is the domain of gof A, and the codomain D, or is the codomain of gof the image of f(A), because gof: A→f(A)⊆C→g(f(A)), that is, it starts in A and ends up in g(f(A)).
Thank you.
Also, let's say we have two functions ƒ, and g, with f:A→B and g:C→D. Let's say that the image of the function f is f(A) ⊆ C. That way, we made sure that gof is defined. So, do we write gof: A → D, that is, is the domain of gof A, and the codomain D, or is the codomain of gof the image of f(A), because gof: A→f(A)⊆C→g(f(A)), that is, it starts in A and ends up in g(f(A)).
Thank you.