quick math question

[jh311]

So i'm a little confused and rusty on how to to do a problem like the following:

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

my question is how do you find F(x)? it says the answer is x^2. Please help, the explanation doesn't tell you how to derive this... it's been a while since i took math. Any help would be appreciated, thanks.

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[Maygyver]

Alright, G(F(x)) is telling you that you want to put F(x) into every time you see x in the G(x) equation essentially.

So, you have G(x)=x-3
What can you put into that x to make a new equation that is x^2-3? x^2

 

[Streetwolf]

So i'm a little confused and rusty on how to to do a problem like the following:

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

my question is how do you find F(x)? it says the answer is x^2. Please help, the explanation doesn't tell you how to derive this... it's been a while since i took math. Any help would be appreciated, thanks.

Poster above me gave one way to think about it. Mathematically, do this:

You have to find F(x) with the statements that G(F(x)) = x^2 - 3 and G(x) = x-3. What does this mean? It means you plug some function F(x)... the one we are looking for... into 'x' which is in G(x) and come out with x^2 - 3.

In other words we are looking for 'y' such that y - 3 = x^2 - 3. Find y in terms of x.

When you do it you get y = x^2.