Given: $$ \mathbf{g}(x)=-1+\sqrt{x} $$. Determine the inverse of $$ \mathbf{g}(x) $$ in the form $$ \mathbf{g}^{-1}(x)=\ldots $$

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To find the inverse of the function $$ \mathbf{g}(x) = -1 + \sqrt{x} $$, we will follow these steps:

1. Replace $$ \mathbf{g}(x) $$ with $$ y $$:
   $$
   y = -1 + \sqrt{x}
   $$

2. Solve for $$ x $$ in terms of $$ y $$:
   $$
   y + 1 = \sqrt{x}
   $$
   $$
   x = (y + 1)^{2}
   $$

3. Replace $$ y $$ with $$ x $$ to express the inverse function:
   $$
   \mathbf{g}^{-1}(x) = (x + 1)^{2}
   $$

Thus, the inverse of $$ \mathbf{g}(x) $$ is:
$$
\mathbf{g}^{-1}(x) = (x + 1)^{2}
$$
The inverse of $$ \mathbf{g}(x) = -1 + \sqrt{x} $$ is $$ \mathbf{g}^{-1}(x) = (x + 1)^{2} $$.

Given: .
Determine the inverse of in the form

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