Question

Which of the following values of x does lie in the domain of the function defined by g(x)=√√2x-7?

(1) x = 0
(3) x = 3
2) x = 2
(4) x = 5

Answer 1

The only value of x that lies in the domain of the given function g(x)=√√2x-7 is x = 5.

Step-by-step explanation:

The function g(x) is defined as g(x) = √(√(2x - 7)). To find the values of x that lie in the domain of this function, we need to ensure that the expression inside the radical is non-negative. If it becomes negative, then it will result in taking the square root of a negative number, which is undefined in real numbers.

Let's consider each option:

1. x = 0: Plugging in x = 0 in the expression, we get g(0) = √(√(-7)). Since -7 is negative, this expression is undefined. So, x = 0 is not in the domain.
2. x = 3: Plugging in x = 3 in the expression, we get g(3) = √(√(2(3) - 7)) = √(√(-1)). Since -1 is negative, this expression is undefined. So, x = 3 is not in the domain.
3. x = 2: Plugging in x = 2 in the expression, we get g(2) = √(√(2(2) - 7)) = √(√(-3)). Since -3 is negative, this expression is undefined. So, x = 2 is not in the domain.
4. x = 5: Plugging in x = 5 in the expression, we get g(5) = √(√(2(5) - 7)) = √(√(3)). Since 3 is positive, this expression is defined. So, x = 5 is in the domain.

From the given options, only x = 5 lies in the domain of the function g(x).

Learn more about Domain of a Function