Question

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

the real numbers would represent the domain of this function? What subset of the real numbers would represent its
range?
Let f(x) = √x − 2

Answer 1

Domain: [2,∞)

Range: [0,∞)

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)=√(2-2)=√(0)=0\\f(3)=√(3-2)=√(1)=1\\f(4)=√(4-2)=√(2)\\f(5)=√(5-2)=√(3)\\f(6)=√(6-2)=√(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,∞)