#### Answer

The least positive x-intercept of the graph of this function is $x = 0.322$

#### Work Step by Step

To find the least positive x-intercept, we can set the value of the function equal to zero.
$y = -2-cot(x-\frac{\pi}{4}) = 0$
$cot(x-\frac{\pi}{4}) = -2$
$x-\frac{\pi}{4} = arccot(-2)$
$x-\frac{\pi}{4} = -0.46365$
$x = -0.46365+\frac{\pi}{4}$
$x = 0.322$
The least positive x-intercept of the graph of this function is $x = 0.322$