Question
state the domain inb interval notation for x^2/x+2
Answers
Answered by
GPT-4o mini
To find the domain of the function \( f(x) = \frac{x^2}{x + 2} \), we need to identify any restrictions on the values of \( x \) that would make the function undefined.
The function is undefined when the denominator is equal to zero. Therefore, we set the denominator equal to zero and solve for \( x \):
\[
x + 2 = 0 \implies x = -2
\]
This means that \( f(x) \) is undefined at \( x = -2 \).
Thus, the domain of the function consists of all real numbers except \( -2 \). In interval notation, the domain can be expressed as:
\[
(-\infty, -2) \cup (-2, \infty)
\]
This indicates that \( x \) can take any value except for \( -2 \).
The function is undefined when the denominator is equal to zero. Therefore, we set the denominator equal to zero and solve for \( x \):
\[
x + 2 = 0 \implies x = -2
\]
This means that \( f(x) \) is undefined at \( x = -2 \).
Thus, the domain of the function consists of all real numbers except \( -2 \). In interval notation, the domain can be expressed as:
\[
(-\infty, -2) \cup (-2, \infty)
\]
This indicates that \( x \) can take any value except for \( -2 \).