Given that the operation & is defined by \(x\&y = \frac{x-y}{x-1}\) and \((-3)\&q=2\) and we need to find the value of q

To find \((-3)\&q\) we need to compare what is before and after the & in \((-3)\&q\) and \(x\&y\)

=> We need to substitute x with -3 and y with q in \(x\&y = \frac{x-y}{x-1}\) to get the value of \((-3)\&q\)

=> \(-3\&q = \frac{-3-q}{-3-1}\) = \(\frac{-(3+q)}{-4}\) = \(\frac{3+q}{4}\) = 2 (Given)

=> 3+q = 4*2 = 8
=> q = 8-3 = 5

So, Answer will be D
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters