Find the domain for the function f(x) = the quotient of the square root of the quantity x minus 3 and the quantity x minus 5.

The domain is (-∞, 3] and (5, ∞)

Step-by-step explanation:

The given function is

In order to find the domain, the denominator cannot be zero and quotient must not be a negative number.

Here the denominator is x - 5

Which must be greater than zero.

x - 5 > 0

x > 5

The numerator must be less than or equal to 0.

x - 3 ≤ 0

x ≤ 3

Therefore, the domain is (-∞, 3] and (5, ∞)

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step-by-step explanation: