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)**