Find the domain and range of the following real functions f(x)=|x+1|/x-2

Question

Find the domain and range of the following real functions

f(x)=\(\frac{|x+1|}{x-2}\)

Answer 1

Given, f (x) = \(\frac{x+1}{x-2}\)

Domain: We known that f (x) is defined when 

x – 2 ≠ 0 i.e., x ≠ 2 

∴ The Domain is all values of x that makes the expression defined 

i.e., Domain of f = R – {2} 

Range: Let y = f(x) 

∴ y = \(\frac{x+1}{x-2}\)

Y ( x– 2) = x + 1 

 x (y – 1) = 2y + 1 

 x = \(\frac{2y+1}{y-1}\)

∵ x is defined, when y – 1 ≠ 0 i. e., y ≠ 1 

∴ Range of f = R – {1}