Show that `f: [-1, 1] ->R`, given by `f(x)=x/((x+2)`is one- one . Find the inverse of the function `f: [-1, 1]→ S where S is the Range of f.`

Explanation

To show that the function \( f: [-1, 1] \to \mathbb{R} \) defined by \( f(x) = \frac{x}{x + 2} \) is one-to-one and to find its inverse, we can follow these steps:

### Step 1: Show that \( f \) is one-to-one

A function \( f \) is one-to-one if \( f(x_1) = f(x_2) \) implies \( x_1 = x_2 \).

Let \( f(x_1) = f(x_2) \). Then we have:

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