Review question

# Can we sketch the graph of $g \colon x \to x - [x]$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5764

## Question

For any real number $x$, $[x]$ denotes the greatest integer not exceeding $x$; e.g. $[3.6] = 3$, $[2] = 2$, $[-1.4] = -2$, etc. Functions $f$ and $g$ are defined on the domain of all real numbers as follows: $\begin{equation*} f \colon x \to [x]; \quad g \colon x \to x - [x]. \end{equation*}$

Find the ranges of $f$ and $g$, and sketch the graph of $g$.

Determine the solution sets of the equations

1. $f(x) = g(x),\qquad$ (ii) $fg(x) = g\,f(x)$.