injectivity

1. Injectivity and surjectivity of a funcion

Hi, can anyone explain me how to calculate surjectivity and injectivity of a function on a following example f(x) = -x^2 + 3 I know that the function is infective if f(x1) = F(x2) = -x^2+3 = -x^2+3 so -x^2 = -x^2 (hope that's correct) and if I take f(3) = -6 and f(-3) = -6 so the function is...
2. The injectivity of a function defined on a set of partitions

Hello. My name is Michael, I'm a freshman CS student and I'm stuck with this problem. I could really use your help: Let T be a non empty set, and let A and B two sets belonging to P(T), the set of partitions of T ( whatever x belongs to P(T), the complement of x = T - x ) Now, let f be a...
3. Injectivity of Holomorphic function

Let U be an open disk around the origin in \mathbb{C}. Suppose f:U \rightarrow \mathbb{C} is holomorphic on U ,f(0) = 0 and f'(0) = 1. I want to show that there exists a neighborhood V of 0, V \subset U, so that f is injective on V. Anybody can help?
4. composite functions and their injectivity and surjectivity

Here is the question: let f : A \rightarrow B and g : B \rightarrow C be functions. i) show that if g \circ f is injective, then f is injective ii) show that if g \circ f is surjective, then g is surjective. Here is what I have so far: g \circ f : A \rightarrow C. Now assume that g \circ...
5. Injectivity of the scalar product

I want to show that \hat{A}: V^* \times V \rightarrow \mathbb{R} (where V is a vector space and V^* is it's dual space) defined by: \hat{A}(v^*,v) \equiv <v^*, Av> is injective. I have a proof from a book, but I don't quite understand what it's doing. It starts by: Haven't they...
6. Theorem on Surjectivity and Injectivity

Hi, I need a help on a proof on this theorem: Given non-empty finite sets X and Y with |X| = |Y|, a function X -> Y is an injection if and only if it is a surjection.
7. injectivity and surjectivity (onto and one-one)

I was going over my assignment to study for the upcoming midterm, and I thought I had a grasp on surjectivity and injectivity...I don't. Can someone tell me where I went wrong in proving these to 'jectives'. define g:integers -> integers be defined by g(n)=4n-5. is it injective...
8. Injectivity and Surjectivity

Let f: X \to Y be a function. Prove that (i) f is injective \Leftrightarrow \overrightarrow{f} is injective \Leftrightarrow \overleftarrow{f} is surjective. (ii) f is surjective \Leftrightarrow \overleftarrow{f} is surjective \Leftrightarrow \overleftarrow{f} is injective. So...