Find \( f+g, f-g, f . g \) and \( \frac{f}{g} \) for the following functions if \( f: \mathbf{R}...

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Find \( f+g, f-g, f . g \) and \( \frac{f}{g} \) for the following functions if \( f: \mathbf{R} \rightarrow \mathbf{R} \) and \( g: \mathbf{R} \rightarrow \mathbf{R} \)
\[
f(x)=\sqrt{1+x}, g(x)=\sqrt{1-x}
\]
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