# 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.