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 excludes values that make the denominator zero, while for radical functions, it excludes values that result in taking the square root of a negative number.
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Square Root Function
A square root function, such as √(x - 2), is defined only for non-negative values of the expression inside the square root. This means that the expression must be greater than or equal to zero, which leads to the condition x - 2 ≥ 0, or x ≥ 2, to ensure the output is real.
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Rational Function
A rational function is a function that can be expressed as the ratio of two polynomials. In the case of g(x) = √(x - 2)/(x - 5), the denominator (x - 5) cannot be zero, which means x cannot equal 5. This restriction must be considered when determining the overall domain of the function.
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