Question

Find the domain of the function
f(x) = 1 / | [3x - 2] | , where [•] is greatest integer function. ​

Answer 1

Step-by-step explanation:

We have,

$f(x) = \frac{1}{ |[3x - 2] | }$

Here, $[3x-2]$ must not equals to 0, because if it becomes 0, them, the function will not be defined,

$[3x - 2] \not= 0$

$\implies3x - 2 \not \in [ 0 , 1)$

$\implies3x \not \in [ 0 + 2 , 1 + 2)$

$\implies3x \not \in [ 2 , 3)$

$\implies \: x \not \in \bigg[ \frac{2}{3} , \frac{3}{ 3} \bigg)$

$\implies \: x \not \in \bigg[ \frac{2}{3} , 1 \bigg)$

So,

$\tt \: dom \{f(x) \} \in \: R - \bigg [ \frac{2}{3} , 1 \bigg)$