Let \( \mathbf{R} \) be the set of all real numbers. Find \( g \circ f \) and \( f \circ g \) wh...

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Let \( \mathbf{R} \) be the set of all real numbers. Find \( g \circ f \) and \( f \circ g \) when \( f: \mathbf{R} \rightarrow \mathbf{R} \) and \( g: \mathbf{R} \rightarrow \mathbf{R} \) are defined by \( f(x)=x+1 \) and \( g(x)=|x| \) for all \( x \in \mathbf{R} \)
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