Question

The inverse of f(x)=2x-1/x+5 may be writeen in the form f^-1(x)=ax+b/cx+d where a,b,c, and d are real numbers. Find a/c. Thank you!

Answer 1

You probably meant:
f(x) = (2x-1)/(x+5)
I will assume that

then
y = (2x-1)/(x+5)
we form the inverse by interchanging x and y
x = (2y-1)/(y+5)
xy + 5x = 2y -1
now solve this for y

xy - 2y = -5x - 1
y(x-2) = -5x - 1
y = f^-1 (x) = (-5x - 1)/(x - 2)

so by comparison,
a = -5
b = -1
c = 1
d = -2

of course we could also write our inverse as
f^-1 (x) = (5x+1)/(-x+2)
all you would have to do is take the opposite of all the a,b, ...'s