Two blocks, M1 and M2, are connected by a massless string that passes over a massless pulley as shown in the figure. M2, which has a mass of 19.0 kg, rests on a long ramp of angle =31.0∘. Friction can be ignored in this problem. Determine the mass 1 of block M1 for which the two blocks are in equilibrium (no acceleration).
If the actual mass of M1 is 5.00 kg and the system is allowed to move, what is the acceleration of the two blocks? A positive acceleration corresponds to M2 moving up the incline.
What distance does block M2 move in 2.00 s?

I tried it but very hard to get the answer sorry

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .