Find the inverse of the function `f: [-1,1] to [-1,1],f(x) =x^(2) xx sgn (x).`

Explanation

To find the inverse of the function \( f: [-1,1] \to [-1,1] \) defined by \( f(x) = x^2 \cdot \text{sgn}(x) \), we will follow these steps:

### Step 1: Understand the function
The function \( f(x) = x^2 \cdot \text{sgn}(x) \) can be expressed in piecewise form:
- For \( x > 0 \): \( f(x) = x^2 \)
- For \( x = 0 \): \( f(x) = 0 \)
- For \( x < 0 \): \( f(x) = -x^2 \)

...