Question

Domain of function f given by

f(x) = 2 –|x – 5| is​

Answer 1

Answer :-

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]Read more on Sarthaks.com - https://www.sarthaks.com/890664/the-domain-and-range-of-the-function-f-given-by-f-x-2-x-5-is

step by step explanation:-

Given: f(x) = 2–|x −5| To find: the domain and range of function Explanation: So the domain of a function consists of all the first elements of all the ordered pairs, i.e., x, so we have to find the values of x to get the required domain Given, f(x) = 2–|x −5| Now x is defined for all real numbers Hence the domain of f is R And the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range Now we know |x-5|≥0 or -|x-5|≤0 Adding 2 we get 2-|x-5|≤2 ⇒ f(x)≤2 Hence the range of f = (-∞, 2] Hence the correct answer is option (B)Read more on Sarthaks.com - https://www.sarthaks.com/890664/the-domain-and-range-of-the-function-f-given-by-f-x-2-x-5-is