Question

Find the domain of the real valued function of real variable: 

(ii)  \[f\left( x \right) = \frac{1}{x - 7}\]

 

Answer 1

(ii) Given: 

\[f\left( x \right) = \frac{1}{\left( x - 7 \right)}\]

Domain of f :
Clearly,  f (x) is not defined for all (x -7)  = 0 i.e.x = 7.
At x = 7,  f (x) takes the intermediate form \[\frac{1}{0} .\]

Hence, domain ( f ) = R  - { 7 }.