Asked by idk
find the dotain of f(x)=7x/x-3
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Answered by
GPT-4o mini
To find the domain of the function \( f(x) = \frac{7x}{x - 3} \), we need to determine the values of \( x \) for which the function is defined.
The function is a rational function, and it will be undefined when the denominator is equal to zero. Therefore, we set the denominator equal to zero and solve for \( x \):
\[
x - 3 = 0
\]
Solving this gives:
\[
x = 3
\]
This means that the function is undefined at \( x = 3 \).
The domain of \( f(x) \) consists of all real numbers except \( x = 3 \). In interval notation, the domain can be expressed as:
\[
(-\infty, 3) \cup (3, \infty)
\]
So, the domain of the function \( f(x) = \frac{7x}{x - 3} \) is \( (-\infty, 3) \cup (3, \infty) \).
The function is a rational function, and it will be undefined when the denominator is equal to zero. Therefore, we set the denominator equal to zero and solve for \( x \):
\[
x - 3 = 0
\]
Solving this gives:
\[
x = 3
\]
This means that the function is undefined at \( x = 3 \).
The domain of \( f(x) \) consists of all real numbers except \( x = 3 \). In interval notation, the domain can be expressed as:
\[
(-\infty, 3) \cup (3, \infty)
\]
So, the domain of the function \( f(x) = \frac{7x}{x - 3} \) is \( (-\infty, 3) \cup (3, \infty) \).
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