Find the domain and range of the following real functions f(x)=4-x/x-4

Question

Find the domain and range of the following real functions

f(x)=\(\frac{4-x}{x-4}\)

Answer 1

Given, f (x) = \(\frac{4-x}{x-4}\) 

Domain: Clearly, f (x) is defined for all x ∈ R expect 

x = 4 

∴ Domain of f = R – {4 } = (−∞, 4),∪ (4, ∞) 

Range: Let y = f(x) 

⇒y = \(\frac{4-x}{x-4}\) 

⇒ y = \(\frac{-(x-4)}{x-4}\) = −1 

∴ Range of f = {– 1}