91Ó°ÊÓ

Domain is the value of x on which the function is defined. We are given with a graph so in graph domain will be the set of all points on x-axis for which the function is defined.

Since we can see clearly that the graph is defined over $x∈[-8,6]$but hold on,

we have some critical points on which we have to check the value of f(x) is valid or not.

these are, $x=-6,-4,2,4$.

Firstly, at $x=-6$the graph goes to $∞$so it must not be in the domain of $f\left(x\right)$.

Secondly, at $x=-4$the value of $f\left(x\right)$is 2 so it will be inclusive in the domain.

Next, $x=2$here also the value of $f\left(x\right)$is 3 so it will also be inclusive in the domain.

Finally, $x=4$here we can clearly see that it is open so it will not be the part of domain.

From step 2 we conclude that

$x∈\left\{\right(-8,-6)∪(-6,-4)∪(-4,2)∪(2,4)∪(4,6\left)\right\},$

and we see that we have to include $x=-8,-4,2,6$these in the domain so final domain will be,

$$\begin{gathered} x∈[-8,-6)∪(-6,4)∪(4,6], \\ or, \\ x∈[-8,6]-\{-6,4\} \end{gathered}$$