Question

Find domain and range of the following function. f(x)=√(x-5)/(x-10)

Answer 1

Answer:

Given: f (x) = 1/√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) = 1/√x−5 . Now for real value of x-5≠0 and x-5>0 ⇒ x≠5 and x>5 Hence the domain of f = (5, ∞) 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 for this function x-5>0 taking square root on both sides, we get √x−5 > 0 Or 1/√x−5 > 0 Or f(x)>0 ⇒ f(x)∈(0, ∞) Hence the range of f = (0, ∞)Read more on Sarthaks.com - https://www.sarthaks.com/890528/find-the-domain-and-range-of-the-function-f-x-1-x5