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 and radical functions, certain restrictions apply, such as avoiding division by zero and ensuring that expressions under a square root are non-negative.
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Square Root Function
A square root function is defined only for non-negative values. Therefore, when analyzing the function f(x) = √(2x/(x + 1) - 1), it is essential to set the expression inside the square root greater than or equal to zero to determine valid x-values.
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Rational Expressions
Rational expressions are fractions where the numerator and denominator are polynomials. In this case, the expression 2x/(x + 1) must be examined to ensure that the denominator does not equal zero, as this would make the function undefined. Thus, x + 1 ≠ 0 must be considered.
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