Inverse function?

Question

.........ax+b
f(x)= ------ ..............find the inverse function
.........cx+d

ad not equal to bc

(the periods don't mean anything, I just needed to get the equation in the right spot.)

will you show me how to work this problem out?

Answer 1

Find the inverse function of

y = f(x) = (ax + b) / (cx + d)

Swap the variables and solve for y.

x = (ay + b) / (cy + d)
(cy + d)x = ay + b
cxy + dx = ay + b
cxy - ay = b - dx
(cx - a)y = b - dx
y = (b - dx) / (cx - a)

The inverse function is:

f¯¹(x) = (b - dx) / (cx - a)

Answer 2

f(x) = (ax + b)/(cx + d)
x = (ay + b)/(cy + d)
cxy + dx = ay + b
y(cx - a) = b - dx
f^-1(x) = (b - dx)/(cx - a)

Answer 3

y(cx+d) =ax+b so x(a-cy) =dy-b and
x=(dy-b)/(a-cy)
chamge x and y
so
y= (dx-b)/(a-cx)