Question
The domain of \( \mathrm{h}(\mathrm{x})=\sqrt{-\mathrm{x}}+6 \) is (Type your answer in interval notation
Ask by Gough Burton. in the United States
Feb 26,2025
Upstudy AI Solution
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Answer
The domain of \( h(x) = \sqrt{-x} + 6 \) is \( (-\infty, 0] \).
Solution
For h(x) to be defined, the expression inside the square root must be greater than or equal to 0:
–x ≥ 0
Multiplying both sides of the inequality by –1 (and reversing the inequality sign) gives:
x ≤ 0
So, the domain of h(x) is all numbers x such that x is less than or equal to 0. In interval notation, this is:
(-∞, 0]
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Simplify this solution Mind Expander
The expression inside the square root, \(-\mathrm{x}\), must be greater than or equal to zero for the function to be defined. This means \(-\mathrm{x} \geq 0\) or \(\mathrm{x} \leq 0\). Therefore, the domain of \(\mathrm{h}(\mathrm{x})\) consists of all non-positive real numbers. In interval notation, this is written as \((- \infty, 0]\). For all you math enthusiasts out there, remember that when dealing with square roots, ensuring that the radicand (the expression inside the root) is non-negative is essential. Otherwise, you'll be venturing into the realm of imaginary numbers, which is a whole different universe of math! Keep those roots real!
