Question
What is the domain of the function y equals StartFraction x over x plus 1 EndFraction?
Answer options with 5 options
A.
all real numbers less than negative 1
B.
all real numbers except negative 1
C.
all real numbers greater than negative 1
D.
all real numbers except 0
E.
all real numbers greater than 0
Answer options with 5 options
A.
all real numbers less than negative 1
B.
all real numbers except negative 1
C.
all real numbers greater than negative 1
D.
all real numbers except 0
E.
all real numbers greater than 0
Answers
GPT-4o mini
To find the domain of the function \( y = \frac{x}{x + 1} \), we need to identify any values of \( x \) that would make the denominator zero, as these are the restrictions on the domain.
The denominator is \( x + 1 \). To find when this is equal to zero, we set it to zero and solve for \( x \):
\[
x + 1 = 0 \implies x = -1
\]
Thus, the function is undefined when \( x = -1 \). Therefore, the domain of the function includes all real numbers except \( -1 \).
Based on this analysis, the correct answer is:
**B. all real numbers except negative 1**
The denominator is \( x + 1 \). To find when this is equal to zero, we set it to zero and solve for \( x \):
\[
x + 1 = 0 \implies x = -1
\]
Thus, the function is undefined when \( x = -1 \). Therefore, the domain of the function includes all real numbers except \( -1 \).
Based on this analysis, the correct answer is:
**B. all real numbers except negative 1**