The inverse function of the function above is f(x) = 4x + 8
You can find the inverse to any function by switching the x and f(x) values. After that, solve for the new f(x) value. The result will be the inverse function. The step-by-step process for this one is done below for you.
f(x) = 1/4x - 2 ----> Start by switching the f(x) and x
x = 1/4f(x) - 2 ----> Now add 2 to both sides
x + 2 = 1/4f(x) ----> Now multiply both sides by 4
f(x) = 4x + 8
Now that you've solved it for the new f(x), you have your inverse function.