Question
Find the domain of the function. (Enter your answer using interval notation.) \[ f(x)=-5 x \] \( x \)
Ask by Lawson Stanley. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The domain of the function \( f(x) = -5x \) is all real numbers, which is written as \( (-\infty, \infty) \).
Solution
To find the domain of the function \( f(x) = -5x \), we need to determine the set of all possible values of \( x \) for which the function is defined.
1. **Identify the function type**: The function \( f(x) = -5x \) is a linear function. Linear functions are defined for all real numbers.
2. **Determine restrictions**: There are no restrictions on \( x \) in this case, as there are no denominators that could be zero, no square roots of negative numbers, or logarithms of non-positive numbers.
3. **Conclusion**: Since there are no restrictions, the domain of the function is all real numbers.
In interval notation, the domain is expressed as:
\[
(-\infty, \infty)
\]
Thus, the domain of the function \( f(x) = -5x \) is \( (-\infty, \infty) \).
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Simplify this solution The Deep Dive
The function \( f(x) = -5x \) is a linear function, which means its graph is a straight line. Linear functions are defined for all real numbers because you can plug any real number into the equation, and it will yield a valid output. Therefore, the domain of the function is all real numbers. In interval notation, the domain can be expressed as: \[ (-\infty, \infty) \] Another way to understand this is to think of the function as an infinitely long line on a graph, extending both left and right without any breaks or restrictions. So, whether you choose \( -1000 \), \( 0 \), or \( 99999 \), you can always compute a valid \( f(x) \)!
