K = { (2, 1), (3, 2), (4, 1), (5, 3) } Is K-1 a function and why?

The domains for this equation are (2,3,4,5) and the ranges for these equations are (1,2,1,3), so because there is no repetition for the x values, then k,-1 is a function. I say this because (2,1) = (-2,-1), (3,2) = (-3,-2), (4,1) = (-4,-1), and (5,3) = (-5,-3), so there is still no repeating x's. so, yes

If your question regards K⁻¹, the inverse of the function K, then the answer is, ...

... No. K⁻¹ is not a function.

The range of K is {1, 2, 1, 3} which includes 1 twice. This would be the domain of the inverse relation. A relation that has repeated values in its domain is not a function.