Find the codomain of this function without using graphs f(x) = \sqrt{x {}^(2) - 9}

Question

Find the codomain of this function without using graphs f(x) =
`\sqrt{x {}^(2) - 9}`

Answer 1

To know the domain of the function without using graphs, we have to remember that negative roots results in imaginary numbers. Thus, to do that we have to equal the expression inside the root to 0:

`x^2-9=0`

Solving for x:

`x^2=9`
`\sqrt[]{x^2}=√(9)`
`x=\pm3`

Then, the domain is:

`\: (-\infty\: ,\: -3\rbrack\cup\: \lbrack3,\: \infty\: )`

Answer:

`(-\infty\: ,\: -3\rbrack\cup\: \lbrack3,\: \infty\: )`