Image of Element under Mapping/Examples/Images of Various Numbers under x^2+2x+1 in Limited Range

Examples of Images of Elements under Mapping
Let $f: \closedint 0 1 \to \R$ be the mapping defined as:


 * $\forall x \in \closedint 0 1: \map f x = x^2 + 2 x + 1$

where $\closedint 0 1$ denotes the closed real interval from $0$ to $1$.

The images of various real numbers under $f$ are: