Review question

# Can we draw the graph of $\left| x + [x] \right|$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5362

## Question

A function $f$ is defined on $\mathbb{R}$ by $\begin{equation*} f \colon x \to \left| x + [x] \right| \end{equation*}$

where $[x]$ indicates the greatest integer less than or equal to $x$, e.g. $[3] = 3$, $[2.4] = 2$, $[-3.6] = -4$. Sketch the graph of the function for $-3 \le x \le 3$. What is the range of $f$? Is the mapping one-one?

The function $g$ is defined by $g \colon x \to \left| x + [x] \right|$, $x \in \mathbb{R}_+$, $x \notin \mathbb{Z}_+$. Find the rule and domain of the inverse function $g^{-1}$.