Question

why is the graph of an inverse of a function flipped over the y=x instead of another line?

Answer 1

because you swap every x and y and then solve for y to get the inverse

Answer 2

when you swap every x and y, then solve for y, it's effectively the same as reflecting everything over y = x

Answer 3

Because basically the definition of inverse function is if \(y=f(x)\), then inverse function would be \(f^{-1}(y)=f^{-1}(f(x)) = x\).

Note that x and y got swapped, hence the reason of it being flipped over the \(y=x\) line.