Let `f:[-1,oo]vec[-1,)` is given by `f(x)=(x+1)^2-1,xgeq-1.` Show that `f` is invertible. Also, find the set `S={x :f(x)=f^(-1)(x)}dot`

Explanation

To solve the problem, we need to show that the function \( f \) is invertible and then find the set \( S = \{ x : f(x) = f^{-1}(x) \} \).

### Step 1: Define the function
The function is given by:
\[ f(x) = (x + 1)^2 - 1 \quad \text{for } x \geq -1 \]

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