The maximum distance visible on Earth is calculated using the formula
= your initial height and
= your secondary height
In this case,
represents the height of the periscope and
denotes the height of the ship, leading us to a distance of 832.45553203368 feet. However, rounding to the nearest mile yields the answer as 
If there are any discrepancies, please inform me and I will recalculate!
The inverse function is defined as h(x) = 4x + 48. To derive it from f(x) = 1/4x - 12, substitute y = f(x) and rearrange the equation to isolate x as shown, leading to h(x).