Question

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

Answer 1

domain:
`x\leq -7, x\geq 3`

Explanation:

`f(x)=√(x^2+4x-21)`

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

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

Therefore,

`f(x)=√((x-3)(x+7))`

`\implies f(x)=√((x-3))√((x+7))`

Find non-negative values for radicals:

`√((x-3)) \implies x\geq 3`

`√((x+7)) \implies x\leq -7`

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