Ivan Shishkin, Birch Grove

Injective map

Definition / Other / Stub

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An injective map is a map which has at least one unique preimage for each element of its set of destination.

Formal definition

For two sets AA and BB, the map f:A→Bf: A \rightarrow B is injective if and only if, we have:
∀y∈B\forall y \in B, there is at least one x∈Ax \in A such as f(x)=yf(x)=y.

Practice this concept with exercises

    1. Soient (a,b)∈R∗×R(a,b) \in \mathbb R^{^{*}} \times \R, et l’application f:x∈R⟼ax+b∈Rf : x \in \R \longmapsto ax+b \in \R est injective.

    2. Soit a∈Ra\in\mathbb R. Sur quel intervalle I⊂R∖{a}I\subset\mathbb R\setminus\{a\} l’application g∈I⟼1(x−a)2∈Rg\in I\longmapsto \frac{1}{(x-a)^2}\in\mathbb R est-elle injective ?

    3. À quelle condition sur (a,b,c)∈R3(a,b,c) \in \R^{3} l’application h:x∈R⟼ax2+bx+c∈Rh : x \in \R \longmapsto ax^{2}+bx+c \in \R est-elle injective ?

    Open exerciseDifficulty 17/100 · 0 solutions · 0 hints
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