What is the domain of the given function?Responses{y | y=−7,−6,−2,−1, 0, 1, 3, 9}start set y such that y is equal to negative 7 comma negative 6 comma negative 2 comma negative 1 comma 0 comma 1 comma 3 comma 9 end set{x | x=−7,−6,−2,−1, 0, 1, 3, 9}start set x such that x is equal to negative 7 comma negative 6 comma negative 2 comma negative 1 comma 0 comma 1 comma 3 comma 9 end set{x | x=−6,−1, 0, 3}start set x such that x is equal to negative 6 comma negative 1 comma 0 comma 3 end set{y | y=−7,−2, 1, 9}
Question
What is the domain of the given function?Responses{y | y=−7,−6,−2,−1, 0, 1, 3, 9}start set y such that y is equal to negative 7 comma negative 6 comma negative 2 comma negative 1 comma 0 comma 1 comma 3 comma 9 end set{x | x=−7,−6,−2,−1, 0, 1, 3, 9}start set x such that x is equal to negative 7 comma negative 6 comma negative 2 comma negative 1 comma 0 comma 1 comma 3 comma 9 end set{x | x=−6,−1, 0, 3}start set x such that x is equal to negative 6 comma negative 1 comma 0 comma 3 end set{y | y=−7,−2, 1, 9}
Solution
The domain of a function is the set of all possible input values (typically represented by x) that will produce a valid output value. In the given function, the domain is represented by the set of x values.
From the given sets, we have three sets of x values:
- {x | x = -7, -6, -2, -1, 0, 1, 3, 9}
- {x | x = -6, -1, 0, 3}
- {y | y = -7, -2, 1, 9} - This set is not relevant to the domain as it is a set of y values, not x values.
So, the domain of the function is the union of the first two sets of x values, which is:
{x | x = -7, -6, -2, -1, 0, 1, 3, 9, -6, -1, 0, 3}
After removing the duplicates, we get:
{x | x = -7, -6, -2, -1, 0, 1, 3, 9}
So, the domain of the given function is all x such that x equals -7, -6, -2, -1, 0, 1, 3, or 9.
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