Question

11. What is the domain of the function? Please show how you solved it and explain.

Answer 1

Answer:

domain:  $x\leq -7, x\geq 3$

Step-by-step explanation:

$f(x)=\sqrt{x^2+4x-21}$

Factor $x^2+4x-21$:

$x^2+4x-21=(x-3)(x+7)$

Therefore,

$f(x)=\sqrt{(x-3)(x+7)}$

$\implies f(x)=\sqrt{(x-3)}\sqrt{(x+7)}$

Find non-negative values for radicals:

$\sqrt{(x-3)} \implies x\geq 3$

$\sqrt{(x+7)} \implies x\leq -7$

Therefore, domain:  $x\leq -7, x\geq 3$