Currently, I am doing transformations on functions, with things like $y=f(x+2)$ representing a transformation of the original function 2 to the left, for example.
However, I am stuck on transforming inverse points. Given a point, say $(-3, 5)$ (made up) on $y=f(x)$, I want to transform it to the graph of $x+1=f(y-1)$.
I noticed the $x$ and $y$ have been switched, so I assume it's a inverse function, so my point is now at $(5, -3)$. I proceeded to isolate $x$, giving me $x=f(y-1)-1$. Then I decided I would need to translate the point 1 right, and 1 down, giving me $(6, -4)$.
However, the answer from the book (from the patterns I see, because I made up the point) is $(4, -2)$. From what I can tell, they left it at $x+1=f(y-1)$ and applied 1 left, and 1 up, the opposite of each to $x$ and $y$. However, I can't tell why.
Could anyone give a me a hint on what I have done wrong? Am I not allowed to move $-1$ over to the right side?