Question
Find the domain of the function. \( f(x)=\sqrt{x-8} \) The domain of \( f(x) \) is \( \square \)
Ask by Evans Barrett. in the United States
Feb 25,2025
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Answer
The domain of \( f(x) = \sqrt{x - 8} \) is all real numbers \( x \) where \( x \geq 8 \), which is written as [8, ∞).
Solution
To find the domain of the function f(x) = √(x - 8), we note that the expression under the square root must be non-negative because the square root of a negative number is not a real number. Therefore, set up the inequality:
x - 8 ≥ 0
Solving this, we get:
x ≥ 8
Thus, the domain of f(x) is all real numbers x such that x is greater than or equal to 8, which is expressed in interval notation as [8, ∞).
The domain of f(x) is [8, ∞).
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To find the domain of \( f(x)=\sqrt{x-8} \), we need to ensure that the expression under the square root is non-negative. This means we want \( x - 8 \geq 0 \). Solving this gives \( x \geq 8 \). Therefore, the domain of \( f(x) \) is all real numbers greater than or equal to 8, expressed in interval notation as \( [8, \infty) \). Remember, when working with square roots, always check that the quantity inside is zero or positive to avoid complex numbers! Misinterpreting or overlooking this can lead to the domain being incorrectly defined, which means no real solutions for your function!
