The domain of the function is R and the range is (–∞, 2].
The function given is f(x) = 2 – |x − 5|.
The domain of a function is the set of all possible input values or x-values.
Since there are no restrictions given in the question, the domain is R, which represents all real numbers.
The range of a function is the set of all possible output values or y-values.
In this case, the function subtracts the absolute value of (x - 5) from 2.
The range will be all values less than or equal to 2, but since there is a subtraction involved, it does not include 2 itself.
Therefore, the range is (–∞, 2].
The probable question may be:
The domain and range of the function f given by f (x) = 2 – |x −5| is
A. Domain = R+, Range = ( – ∞, 1]
B. Domain = R, Range = ( – ∞, 2]
C. Domain = R, Range = (– ∞, 2)
D. Domain = R+, Range = (– ∞, 2]