Answer:
domain: [tex]x\leq -7, x\geq 3[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt{x^2+4x-21}[/tex]
Factor [tex]x^2+4x-21[/tex]:
[tex]x^2+4x-21=(x-3)(x+7)[/tex]
Therefore,
[tex]f(x)=\sqrt{(x-3)(x+7)}[/tex]
[tex]\implies f(x)=\sqrt{(x-3)}\sqrt{(x+7)}[/tex]
Find non-negative values for radicals:
[tex]\sqrt{(x-3)} \implies x\geq 3[/tex]
[tex]\sqrt{(x+7)} \implies x\leq -7[/tex]
Therefore, domain: [tex]x\leq -7, x\geq 3[/tex]
