Question

how can you determine whether the inverse of a function is itself a function? Is there examples of a function whose inverse is a function and a function whose inverse is not a function?

Answer 1

f ( x ) = (x-2)/(x-1)

if y = (x-2)/(x-1)
yx-y= x - 2
yx-x= -2+y
x(y-1)=y-2
x = (y-2)/(y-1)

so g ( x ) the inverse function is also (x-2)/(x-1)

Answer 2

@hba your a life saver ; thanks cutie