Question

Describe the domain of the function. g(x)= 1/√ 3−x

The domain of the function consists of all real numbers x where(Type an inequality.)

Answer 1

The domain of g(x) = 1/√(3-x) is all real numbers x such that x <= 3, because the expression under the square root must be positive or zero.

Step-by-step explanation:

The domain of the function g(x) = 1/√(3-x) consists of all real numbers x for which the expression inside the square root, 3 - x, is positive. This is because the square root of a negative number is not defined within the real numbers. To find the domain, we set the inside of the square root to be greater or equal to zero:
3 - x >= 0
x <= 3

Hence the domain of g(x) can be expressed as the inequality x <= 3.