What is the inverse function of y= 1-x^1/2 / 1+x^1/2?

Question

pls help

Answer 1

y = (1/x - 1)^2

Answer 2

f(x) = [1 - x^1/2] / [1 + x^1/2]

let f(x) = y, then x = f^-1(y).

f(x) = [1 - x^1/2] / [1 + x^1/2] = y

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

1 - y = x^1/2 + yx^1/2 = x^1/2 * (1 + y)

x^1/2 = (1 - y) / (1 + y)

x = [(1 - y) / (1 + y)]^2 = f^-1(y)

f^-1(x) = [(1 - x) / (1 + x)]^2

domain : x is all but -1.

Answer 3

Switch x and y

solve for y

Answer 4

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

so y^-1 is all R