Pergunta
Find the domain of the following rational function. f(x)=(18x)/(x+13) Select the correct choice below and, if necessary, fill in the answer box to complete your c A. The domain of f(x) is restricted to square (Type your answer in interval notation.) B. The domain of f(x) has no restrictions.
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AdrianaMestre · Tutor por 5 anos
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To determine the domain of the rational function \( f(x) = \frac{18x}{x+13} \), we need to identify any values of \( x \) that would make the denominator equal to zero, as division by zero is undefined.<br /><br />The denominator of the function is \( x + 13 \). Setting the denominator equal to zero gives:<br />\[<br />x + 13 = 0<br />\]<br />Solving for \( x \), we get:<br />\[<br />x = -13<br />\]<br /><br />Therefore, the function \( f(x) \) is undefined at \( x = -13 \). The domain of \( f(x) \) includes all real numbers except \( x = -13 \).<br /><br />In interval notation, the domain is:<br />\[<br />(-\infty, -13) \cup (-13, \infty)<br />\]<br /><br />So, the correct choice is:<br />A. The domain of \( f(x) \) is restricted to \( (-\infty, -13) \cup (-13, \infty) \).
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