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...
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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)