Question

The domain and range of this function are not specified. Evaluate the function for several values of x. What subset of

Answer 1

Answer:

Domain: [2,∞)

Range: [0,∞)

Step-by-step explanation:

Domain are the values of x allowed for the function.

In this function, because we have a square root, we cannot have numbers in the domain such that the root contains a negative number, because the function would not be defined in real numbers.

Thus, the domain is:

Domain= x-2 ≥ 0

Domain = x ≥ 2

Or what is the same [2,∞)

And the range is the values that the function returns for every number in the domain. Since our domain is the values of x greater than or equal to two:

$f(2)=\sqrt{2-2}=\sqrt{0}=0\\f(3)=\sqrt{3-2}=\sqrt{1}=1\\f(4)=\sqrt{4-2}=\sqrt{2}\\f(5)=\sqrt{5-2}=\sqrt{3}\\f(6)=\sqrt{6-2}=\sqrt{4}=2\\.\\.\\.\\.$

We can see that the minimum value of y = f (x) is 0 and the greatest number that the function can return to us has no limit, so the range is:

Range: [0,∞)