Question
Find the domain of the following rational function.
f left parenthesis x right parenthesis equals StartFraction 14 x Over x minus 15 EndFraction
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The domain of f(x) is restricted to
enter your response here.
(Type your answer in interval notation.)
B.
The domain of f(x) has no restrictions.
f left parenthesis x right parenthesis equals StartFraction 14 x Over x minus 15 EndFraction
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
The domain of f(x) is restricted to
enter your response here.
(Type your answer in interval notation.)
B.
The domain of f(x) has no restrictions.
Answers
GPT-4o mini
To find the domain of the rational function \( f(x) = \frac{14x}{x - 15} \), we need to identify any values of \( x \) that would make the denominator equal to zero, as those values are not included in the domain.
The denominator is \( x - 15 \). Setting it equal to zero gives:
\[
x - 15 = 0 \implies x = 15
\]
This means that \( x = 15 \) is a restriction, and we cannot use this value in the function.
Thus, the domain of \( f(x) \) is all real numbers except \( 15 \). In interval notation, this can be written as:
\[
(-\infty, 15) \cup (15, \infty)
\]
So, the correct choice is:
A. The domain of \( f(x) \) is restricted to \( (-\infty, 15) \cup (15, \infty) \).
The denominator is \( x - 15 \). Setting it equal to zero gives:
\[
x - 15 = 0 \implies x = 15
\]
This means that \( x = 15 \) is a restriction, and we cannot use this value in the function.
Thus, the domain of \( f(x) \) is all real numbers except \( 15 \). In interval notation, this can be written as:
\[
(-\infty, 15) \cup (15, \infty)
\]
So, the correct choice is:
A. The domain of \( f(x) \) is restricted to \( (-\infty, 15) \cup (15, \infty) \).