Word Count : 321

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The function ( g:\mathbb{R}\setminus{2} \to \mathbb{R} ) is defined by ( g(x) = \frac{x-1}{2-x} ). First, to check if ( g ) is well-defined: the domain is ( \mathbb{R} \setminus {2} ), so ( x \neq 2 ). The denominator ( 2-x ) is nonzero for all ( x \neq 2 ). Therefore, ( g(x) ) is defined for all ( x ) in the domain. Hence, ( g ) is well-defined. Next, to check if ( g ) is _________ ____ _________ ___ ___ _______ _______ ______ _________ _______.
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