Question

Show that f: [-1,1] → R, given by f(x) = \(\frac{x}{(x + 2)}\) is one-one. Find the inverse of the function f : [-1,1] → Range f.

(Hint: For y ∈ Range f, y = \(\frac{x}{(x + 2)}\)for some x in [-1, 1] \(x = \frac{2y}{(1 - y)}\))

Answer 1

Let x₁, x₂ ∈ D_r