thank you so much! but could you explain how you got f(x)= 1+ a-b/x+b? thank you

also, if you don’t mind, could you also explain the line “since x=1 is the asymptote, f^-1(x)= (x+a)/b-1 and hence b= -1”? thank you so much

You do long division will get the partial fraction out...

x=1 is the vertical asymptote. If you have learnt Graphing techniques, you will know.
In short, you make the denominator of that fraction equal to zero, you will get the equation of vertical asymptote.

You typed wrongly in your second comment: denominator should be "x-1", not "b-1".
Since the denominator was written as "x+b", equate it to zero gets x+b=0, rearrange gets x=-b, the equation of the vertical asymptote of x=1, hence -b must be equal to 1, therefore b=-1.

oh ok i get it now, thank you so much for your help!