22tford
22tford 22tford
  • 16-02-2022
  • Mathematics
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11. What is the domain of the function? Please show how you solved it and explain.

11 What is the domain of the function Please show how you solved it and explain class=

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semsee45
semsee45 semsee45
  • 16-02-2022

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]

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