Question

Maksim was asked on a test "What is the domain of the function: f(x) = √(x - 2)? Explain." Maksim responded with "The function f(x) = √(x - 2) has a domain of all real numbers because any number can be put in for x." Explain if Maksim's answer and explanation were correct. Make sure to use at least two pieces of evidence to support your claim. If he is wrong, state the actual domain.

Answer 1

Maksim's answer and explanation are not correct

The actual domain is 2 < x < Infinity

Explanation:

The domain of a function is the set that is made up of the possible inputs of the function

The given function is f(x) = √(x - 2)

Maksim's response for the domain of f(x) is x ∈ R ('x' is a member of the set of all real numbers

The function is not defined when x < 2, at which the expression, x - 2, will become negative, and for which the square root of the negative number is imaginary

Therefore, the domain for which the function is defined is all real numbers larger than 2, which can be presented as follows;

The domain of f(x) = 2 < x < ∞

Therefore Maksim is wrong as the actual domain is limited to 2 < x < ∞.