find the domain g(x)=8x / x^2 -25 the answer should be in interval notation

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You should notice that the domain of the function needs to consist of all values that makes the function to exist.

Hence, you need to notice that the function does not exist if x has the value of a root of denominator, thus, you need to exclude the values of roots of denominator from domain of function.

You need to find the zeroes of denominator such that:

`x^2 - 25 = 0`

You may convert the difference of squares into a special product such that:

`x^2 - 25 = (x - 5)(x + 5)`

You need to solve the equation `(x - 5)(x + 5) = 0`  such that:

`(x - 5)(x + 5) = 0 ` => `{(x - 5 = 0),(x + 5 = 0):}` `=gt {(x = 5),(x = -5):}`

Hence, evaluating the domain of the given function yields `D = `(-oo,-5)U(5,+oo)`

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