Image of Mapping/Examples
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Examples of Images of Mappings
Arbitrary Example
Let $f$ be defined as:
- $\forall x: 0 \le x \le 2: \map f x = x^3$
The image of $f$ is the closed interval $\closedint 0 8$.
Image of $\map f x = x^4 - 1$
Let $f: \R \to \R$ be the mapping defined as:
- $\forall x \in \R: \map f x = x^4 - 1$
The image of $f$ is the unbounded closed interval:
- $\Img f = \hointr {-1} \to$
and so $f$ is not a surjection.
Image of $\map f x = x^2 - 4 x + 5$
Let $f: \R \to \R$ be the mapping defined as:
- $\forall x \in \R: \map f x = x^2 - 4 x + 5$
The image of $f$ is the unbounded closed interval:
- $\Img f = \hointr 1 \to$
and so $f$ is not a surjection.