Question
Give the domain of \( n(x)=|-10-2 x| \) using interval notation.
Ask by Bolton Moreno. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The domain of \( n(x) = |-10 - 2x| \) is all real numbers, which in interval notation is \( (-\infty, \infty) \).
Solution
The function in question is \( n(x) = |-10 - 2x| \).
To determine the **domain** of this function, we need to identify all real numbers \( x \) for which the expression inside the absolute value, \(-10 - 2x\), is defined.
The expression \(-10 - 2x\) is a linear function, and linear functions are defined for all real numbers. There are no restrictions such as divisions by zero or square roots of negative numbers that would limit the domain.
Therefore, the **domain** of \( n(x) \) is all real numbers.
**Interval Notation:**
\[
(-\infty, \infty)
\]
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Simplify this solution Extra Insights
The function \( n(x) = |-10 - 2x| \) is defined for all real numbers since the absolute value function can accept any input without restrictions. This means that there are no values of \( x \) that would cause the function to be undefined. Therefore, the domain of \( n(x) \) in interval notation is: \[ (-\infty, \infty) \] This notation indicates that the function is valid for every possible real number. So, feel free to plug in any value of \( x \) you'd like!
