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Can someone PLEASE explain how to solve this? The fraction at the end completely throws me off!! Pic related:

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Okay... So, essentially \[\huge \frac{f}g(x) = \frac{f(x)}{g(x)}\] is the key to understanding this...
I deducted it and f(x) = 3 and g(x) = 7 But, my answer isn't 7... My answers are: 3 -3 -1 1 I tried dividing 3 by 7 and 7 by 3, but that didn't work.
f(x) = 3? I take it you meant f(-2) indeed, f(-2) = 3 I suggest you retry g(-2)

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I thought: \[\frac{ f }{ g }(-2) = \frac{ f(-2) }{ g }\] Then I'd find f(-2) Then I'd plug in -2 to g(x) and get 7.
Ahh. No. \[\huge \frac{f}g(x) = \frac{f(x)}{g(x)}\\\huge \frac{f}g(-2)=\frac{f(-2)}{g(-2)}\]
It does bug me when they use shorthand notation resulting into unclear stuff... but yeah, that's Maths for you :P
Here is what I did: f(x) = -3x - 3 f(x) = -3(-2) - 3 f(x) = 6 - 3 f(x) = 3 Plug it into g g(x) = 2(3) + 1 g(x) = 7 But the answer isn't seven. Am I doing it wrong?
because you're not supposed to get g(f(-2)) Just g(-2)
\[\frac{ -3(-2) - 3 }{ 2(-2) + 1 }\] Is that it?
\[\frac{ 3 }{ -3 } = -1\]
There you go.
Okay, and can you explain the g(f[4]) thingy?
That's when you first get the result of f(4) and then plug it into g(x)
And if you had f(g[4]) You'd first get g and plug it into f?
You'd first get g(4) and then plug it into f(x) , yes :)
I see. It's all about order. But sometimes it's so unclear ;-;
Hopefully clearer now, if only a little bit :)
Yup! Thanks

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