Suppose that `g(x)=1+sqrt(x) " and " f(g(x))=3+2sqrt(x)+x.` Then find the function `f(x)`.

Explanation

To find the function \( f(x) \) given that \( g(x) = 1 + \sqrt{x} \) and \( f(g(x)) = 3 + 2\sqrt{x} + x \), we can follow these steps:

### Step 1: Substitute \( g(x) \) into \( f(g(x)) \)

We know that \( g(x) = 1 + \sqrt{x} \). Therefore, we can write:
\[ f(g(x)) = f(1 + \sqrt{x}) = 3 + 2\sqrt{x} + x \]
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