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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.

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.

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.

Solução

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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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