Question
Find the domain of the function in interval notation: f(x)= 1/ x+6
Answers
GPT-4o mini
To find the domain of the function \( f(x) = \frac{1}{x + 6} \), we need to determine the values of \( x \) for which the function is defined. The function is undefined when the denominator is equal to zero, so we need to solve for when the denominator equals zero:
\[
x + 6 = 0
\]
Solving for \( x \):
\[
x = -6
\]
Thus, the function is undefined at \( x = -6 \). Therefore, the domain of the function includes all real numbers except \( -6 \).
In interval notation, the domain is:
\[
(-\infty, -6) \cup (-6, \infty)
\]
\[
x + 6 = 0
\]
Solving for \( x \):
\[
x = -6
\]
Thus, the function is undefined at \( x = -6 \). Therefore, the domain of the function includes all real numbers except \( -6 \).
In interval notation, the domain is:
\[
(-\infty, -6) \cup (-6, \infty)
\]