Question
Find the domain of the function. \( f(x)=-9 x+7 \) The domain is \( \square \). (Type your answer in interval notation.)
Ask by Davey Todd. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The domain of \( f(x) = -9x + 7 \) is all real numbers, which in interval notation is \((-\infty, \infty)\).
Solution
The function \( f(x) = -9x + 7 \) is a linear function. Linear functions are defined for all real numbers because there are no restrictions such as divisions by zero or square roots of negative numbers.
**Domain of \( f(x) \):**
All real numbers.
**In interval notation:**
\((-\infty, \infty)\)
\(\boxed{\,(-\infty,\ \infty)\,}\)
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Simplify this solution Extra Insights
The function \( f(x) = -9x + 7 \) is a linear function, which means it is defined for all real numbers. Since there are no restrictions such as square roots or divisions by zero, you can input any value for \( x \) without encountering issues. This means the domain of the function is all real numbers. Thus, the domain is \( (-\infty, \infty) \). In interval notation, it’s represented as \( (-\infty, \infty) \).
