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

Question

Find the domain and range of the following real functions

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

Answer 1

Given, f (x) = \(\frac{|x-1|}{x-1}\) 

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

except x = 1 

∴ Domain of f = R –\(\left\{\overrightarrow{1}\right\}\)

Range: Now, f (x) = \(\frac{x-1}{x-1}\)= 1, when > 1 

And f(x) = \(\frac{-(x-1)}{x-1}\) = −1, when x < 1 

∴ Range of f = {– 1, 1}