Hodges Lane
07/18/2023 · Middle School
Give the domain of \( g(x)=\sqrt{x-14} \) in interval notation \( \square \) Calculator
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Step-by-step Solution
To find the domain of the function \( g(x) = \sqrt{x - 14} \), we need to determine the values of \( x \) for which the expression under the square root is non-negative, since the square root is only defined for non-negative numbers.
Set the expression under the square root greater than or equal to zero:
\[
x - 14 \geq 0
\]
Solving this inequality:
\[
x \geq 14
\]
Thus, the domain of \( g(x) \) is all \( x \) values that are greater than or equal to 14. In interval notation, this is expressed as:
\[
[14, \infty)
\]
So, the domain of \( g(x) = \sqrt{x - 14} \) in interval notation is:
\[
\boxed{[14, \infty)}
\]
Quick Answer
Domain: [14, ∞)
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