Math Destroyer test #2 Question 15 2014 edition

[ballerinacubana]

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if G(F(x))=x^2-3 and G(x)=x-3, find (3). Answer is 9

 

[DAT Destroyer]

First we need to find F(x).we know that G(F(x)) = x^2 - 3 we also know that G(x) = x - 3 so we have G(F(x)) = x^2 - 3 = F(x) - 3we get F(x) = x^2 and therefore F(3) = 9

 

[rlior84]

Thanks

 

[hunyogo]

Thanks

 

[csulapredental]

First we need to find F(x).we know that G(F(x)) = x^2 - 3 we also know that G(x) = x - 3 so we have G(F(x)) = x^2 - 3 = F(x) - 3we get F(x) = x^2 and therefore F(3) = 9

that made no sense.
can u please list more steps i don't get this at all

 

[Lnguyen7]

if G(F(x))=x^2-3 and G(x)=x-3, find (3). Answer is 9

To find F(3), you need to know the function of F(x).

You are given G(x) = x - 3

G[F(x)] means for any x in G(x), you replace x by F(x)
so G[F(x)] = F(x) - 3 (1)

You are also given G[F(x)] = x^2 - 3 (2)

(1)(2) give you G[F(x)] = F(x) - 3 = x^2 - 3 (just like a = b and a = c, so b must be equal c)
Simplify and you get F(x) = x^2

So F(3) = 9