Question

The domain and range of the real function f defined by f(x) = (4 - x)/(x - 4)  is given by 

A. Domain = R, Range = {–1, 1}  

B. Domain = R – {1}, Range = R 

C. Domain = R – {4}, Range = {– 1} 

D. Domain = R – {– 4}, Range = {–1, 1}

Answer 1

Given: f(x) = (4 - x)/(x - 4)

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) = (4 - x)/(x - 4)

Now for real value of

x-4≠0

⇒ x≠4

Hence the domain of f = R-{4}

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

Given,

⇒ f(x) = -1

Hence the range of f = {-1}

Hence the correct answer is option (C)