What is the domain of the function?
y = √5x - 10
A. x ≥ -2
B. x ≤ -2
C. x ≥ 2
D. x ≤ 2
The function is defined for any real value of x that makes the expression inside the square root non-negative, since the square root of a negative number is not a real number. Therefore, we need to solve the inequality:
5x - 10 ≥ 0
Adding 10 to both sides, we get:
5x ≥ 10
Dividing both sides by 5, we get:
x ≥ 2
So the domain of the function is x ≥ 2, which is option C.
To find the domain of the function y = √5x - 10, we need to determine the values of x for which the function is defined.
The square root function is defined for non-negative real numbers. Therefore, we need to find the values of x that make the expression inside the square root non-negative.
In this case, the expression inside the square root is 5x - 10. To find the values of x that make this expression non-negative, we set it equal to zero and solve for x:
5x - 10 ≥ 0.
Adding 10 to both sides of the inequality, we get:
5x ≥ 10.
Dividing both sides by 5, we have:
x ≥ 2.
Therefore, the domain of the function y = √5x - 10 is x ≥ 2.
So, the correct answer is:
C. x ≥ 2.