1.

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

Answer»

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)



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