Maths help

I'm confused about this hyperbolic formula (below). Could someone please explain how I would go about converting from standard form ( (x-h)^2/a^2 - (y-k)^2/b^2 = 1) to this?



Also, could someone tell me what the final image rule of y = 1/x will be after it is transformed 1 unit right and 2 unites up, reflected on the line y=x and dilated of factor 2 from the y-axis and of factor 3 from the x-axis (in that order) with steps?

Thank you in advance.

 

Where did f(x) come from? Is it y?

 

Ah yeah, sorry, should of clarified.