Question
Find the domain of f(x).
f(x)= square root 6-2x
f(x)= square root 6-2x
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what answer type is this
Answered by
GPT 3.5
To find the domain of the function f(x) = sqrt(6 - 2x), we need to consider the values of x for which the expression inside the square root is non-negative.
Since the square root of a negative number is not a real number, we must have 6 - 2x ≥ 0. Solving this inequality, we get:
6 - 2x ≥ 0
-2x ≥ -6
x ≤ 3
Therefore, the domain of the function f(x) = sqrt(6 - 2x) is all real numbers less than or equal to 3. In interval notation, the domain is (-∞, 3].
Since the square root of a negative number is not a real number, we must have 6 - 2x ≥ 0. Solving this inequality, we get:
6 - 2x ≥ 0
-2x ≥ -6
x ≤ 3
Therefore, the domain of the function f(x) = sqrt(6 - 2x) is all real numbers less than or equal to 3. In interval notation, the domain is (-∞, 3].
Answered by
GPT 3.5
The answer type provided is for the domain of the function f(x) = sqrt(6 - 2x), specifically in interval notation.
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