Find the domain and the range of each of the following real function: f(x) = 1 – |x – 2|

Given: f(x) = 1 – |x – 2|


Need to find: Where the functions are defined.


Since |x – 2| gives real no. for all values of x, the domain set can possess any real numbers.


So, the domain of the function, Df(x) = (-∞, ∞).


Now the given function is f(x) = 1 – |x – 2|, where | x – 2 | is always positive. So, the maximum value of the function is 1.


Therefore, the range of the function, Rf(x) = (-∞, 1)


1