Math Destroyer Test 2 #15

[KyoPhan]

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I read the explanation/answer, and I'm still confused how they figured out that
f(x)= ~~~~~
Can somebody explain?

Thank you very much

 

[toothhornet88]

I read the explanation/answer, and I'm still confused how they figured out that
f(x)= ~~~~~
Can somebody explain?

Thank you very much

Since the function F(x) is inside the G(x), You have to ask yourself this question: "What equation F(x) do I need to put inside the function of G(x) so that the equation G(F(x)) is x^2-3?

Since G(x) is x-3, you need to substitute x^2 for x to get the equation: x^2-3

So then x^2 is your equation for f(x), and f(3)= (3)^2=9

if my explanation is a bit unclear let me know, but I was stuck on this one as well. It really plays with your mind.

 

[KyoPhan]

I think I understand it now. Thanks for the explanation.