Question
find the domain of f(x)= 6x/x+3
Answers
GPT-4o mini
To find the domain of the function \( f(x) = \frac{6x}{x + 3} \), we need to identify the values of \( x \) for which the function is defined. The function is undefined when the denominator is equal to zero.
Set the denominator equal to zero and solve for \( x \):
\[
x + 3 = 0
\]
\[
x = -3
\]
Therefore, the function is undefined at \( x = -3 \). The domain of \( f(x) \) includes all real numbers except \( -3 \).
In interval notation, the domain is:
\[
(-\infty, -3) \cup (-3, \infty)
\]
Set the denominator equal to zero and solve for \( x \):
\[
x + 3 = 0
\]
\[
x = -3
\]
Therefore, the function is undefined at \( x = -3 \). The domain of \( f(x) \) includes all real numbers except \( -3 \).
In interval notation, the domain is:
\[
(-\infty, -3) \cup (-3, \infty)
\]