#### Question

# Help me with this inverse function?

How to isolate y on the left side in this function:

x = (y - 1)/(y + 1)

Thank you.

#### Answers

To invert, find "y"

x = (y-1) / (y+1)

x (y+1) = y-1

xy + x = y-1

x+1 = y-xy

x+1 = y (1-x)

y = (x+1)/(1-x)

#1

x = (y - 1)/(y + 1)

Interchange x and y we get

y = (x - 1)/ (x+1) then it is the inverse of the given function.........................Ans

#2

x = (y-1)(y+1) (multiple all terms)

x = y^2+y-y-1 = y^2-1

x+1 = y^2-1+1 (add 1 to both sides of eqn)

x+1 = y^2 (now need to take sq root of both sides)

sqrt(x+1) = y

Since y is a quadratic it has 2 roots:

y1 = -sqrt(x+1)

y2 = +sqrt(x+1)

#3

x (y+1) = y-1

xy +x = y -1

xy - y = -(x+1)

y(x-1) = -(x+1)

y = -(x+1)/(x-1)

#4