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Given the equation: f(x) =1/sqrt(x-3)
We need to find the domain of f(x).
We know that the domain is all x values such that f(x) is defined.
Since f(x) is a quotient, then the denominator can not be zero.
Also, we notice that the denominator is a square root.
Then (x-3) must be positive values.
==> sqrt(x-3) > 0
==> x-3 > 0
==> x > 3
Then the domain is x = ( 3, inf)
f(x) = 1/sqrt(x-3). To find the domain.
The domain of the function f(x) = 1/sqrt(x-3) is the set of all values of x for which the function is defined and is real.
If x is less than 3, then f(x) can not be real. Therefore the x must be greater than or equal to 3 for which f(x) is defined.
Therefore the domain of the function f(x) = 1/sqrt(x-3) is the set {x : x> = 3}.
Or the domain of the function is the interval (3, infinity).
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