Question
Find the domain of the function using interval notation. \[ f(x)=4 \sqrt{x-9} \]
Ask by Watson Erickson. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain of the function is \([9, \infty)\).
Solution
1. For the square root function to be defined, the expression inside the square root must be non-negative. Therefore, we require
\[
x - 9 \geq 0.
\]
2. Solving the inequality:
\[
x \geq 9.
\]
3. In interval notation, the domain of the function is
\[
[9, \infty).
\]
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Simplify this solution Extra Insights
To find the domain of the function \( f(x) = 4 \sqrt{x - 9} \), we need to determine for which values of \( x \) the expression inside the square root is non-negative, because the square root function is only defined for non-negative inputs. This means that: \[ x - 9 \geq 0 \] Solving this inequality gives: \[ x \geq 9 \] Therefore, the domain of the function can be expressed in interval notation as: \[ [9, \infty) \]
