Preimage

Let $f:X \rightarrow Y$ be a map and $A\subseteq X$ . The preimage of $A$ under $f$ is the subset of $X$ defined as:
$f^{-1}(A)=\{x\in X:f(x)\in A\}.$

Practice this concept with exercises

On considère $\begin{array}{rcl} f : \mathbb{R} &\longrightarrow& \mathbb{R} \\ x &\longmapsto & x^{2} \end{array}$ . Déterminer les images réciproques suivantes :
1. $f^{-1}([0, 1])$
2. $f^{-1}([1, 4]$ )
3. $f^{-1}(\mathbb{R_{-}})$
Open exercise

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