Answer
$(-\infty,-0.5]$
$[-0.5,\infty)$
Work Step by Step
We are given the function:
$f(x)=|2x+1|$
Graph the function and apply the Horizontal Line Test.
We notice that there the function fails the Horizontal Line Test on $R$ as a horizontal line intersects the graph in more than one point. We can restrict the function to intervals on which the Horizontal Line Test is checked and the function has inverse. For example:
$(-\infty,-0.5]$
$[-0.5,\infty)$
and any interval included in these two intervals.
The largest intervals are:
$(-\infty,-0.5]$
$[-0.5,\infty)$.
