Given:
[tex]f(x)=\sqrt[]{x^2-9}[/tex]To find the codomain:
We know that,
The Co-domain of the function is the set of all possible values which can come out as a result.
Since,
[tex]\sqrt[]{x^2-9}\ge0[/tex]Thus, f(x) takes all real values greater than or equal to zero.
So, the codomain of the function is,
[tex]\lbrack0,\infty)[/tex]