# Image of Mapping/Examples

## Examples of Images of Mappings

### 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.