Here are the essential concepts you must grasp in order to answer the question correctly.
Domain of a Function
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For rational functions, the domain is typically restricted by values that would make the denominator zero, as division by zero is undefined.
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Rational Functions
A rational function is a function that can be expressed as the ratio of two polynomials. In the case of g(x) = 4/(x - 7), the numerator is a constant (4) and the denominator is a linear polynomial (x - 7). Understanding the structure of rational functions is essential for determining their domains.
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Finding Restrictions
To find the domain of a function, one must identify any restrictions on the input values. For g(x) = 4/(x - 7), the restriction arises from the denominator, which cannot equal zero. Thus, solving the equation x - 7 = 0 reveals that x cannot be 7, leading to the conclusion that the domain excludes this value.
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