When computing the inverse g^(-1), we simply swap all x and y values. So we go from (x,y) to (y,x) effectively. The function g(x) = {(5,3), (2,3), (6,4)} has the inverse g^(-1)(x) = {(3,5), (3,2), (4,6)} this inverse is a relation but it is NOT a function.
Why isn't it a function? Because we have the two points (3,5) and (3,2) with repeated x values. These two points will violate the vertical line test. A function must have all inputs lead to exactly one output. But the input of x = 3 leads to y = 5 and y = 2 simultaneously.
Side Note: The original function g(x) fails the horizontal line test so it is NOT one-to-one, making an inverse function not possible.
