Question

domain of sqrt(1+(3/x))

Answer 1

To determine the domain of the function f(x) = sqrt(1 + (3/x)), we need to consider two conditions:

1. The argument of the square root cannot be negative.
2. Denominator cannot be zero.

First, let's consider the argument of the square root, 1 + (3/x):

1 + (3/x) ≥ 0
3/x ≥ -1
x ≤ -3

So, the first condition tells us that x cannot be less than or equal to -3.

Next, let's consider the denominator:

x ≠ 0

This condition tells us that x cannot be equal to zero.

Therefore, the domain of the function f(x) = sqrt(1 + (3/x)) is all real numbers except for x ≤ -3 and x ≠ 0.