stuck on math problem, functions

[steiner2]

I am stumped on this one from Math Destroyer

if G(F(x))=X^2-3 and G(x)=x-3
find F(3).

I got an answer of 3 but it's not it. Unless orgoman is wrong.

 

[FeralisExtremum]

Answer is 9

G(F(x)) = x^2 - 3
G(x) = x - 3
Find F(3)

So, we need to figure out what f(x) is. We're given g(x), and f(x) inside of g(x). If g(x) is x - 3 and f(x) inside g(x) gives us x^2 - 3, we know that f(x) = x^2

Then we plug 3 into it, 3^2 = 9

 

[LazyP]

Well F(x) = x^2 because since G(x) = x-3, substitue X^2 for x will give you G(F(x)) = (X^2)-3. so F(3) = 9. Is that the answer?

 

[steiner2]

Bah, you guys are both right. I don't know what happened to the "-3" though. Thanks.

 

[FeralisExtremum]

Bah, you guys are both right. I don't know what happened to the "-3" though. Thanks.

The "-3" only appears in g(x), not f(x).

 

[steiner2]

I guess I am used to seeing The G(x) and F(x) both defined. The logical way would be to try to solve F(x) first, then take that result and plug into G(x). I can't see how you guys do it.

-But plugging 3 into F(x) gives 9-3. So G(F(x))=9-3 since G(F(x))=X^2-3...sticking 3 for x gives 9-3
-G(x)=x-3
-therefore, since 9-3=x-3, we have 9=x.

Is that similar?

 

[LazyP]

here is a simple way ....
u know G(F(x))=X^2-3 and G(x)=x-3....
make them equal to each but for x in the G(x) sub it with F(x) so it becomes a G(F(x)), so it will be....
(X^2)-3 = (F(x))-3... there are basically the same equation if and only if (x^2) = (F(x)) so F(3) = 9

hope that helps