Question

Function Notations
Given
f(x) = 2x-7
g(x) = x^2 + x
Find: g(f(x))
g(f(x))=(2x−7)^2+(2x−7)- im confused because of this substituting part, why is it substitute like this? :S

Answer 1

Whenever you see it that way, you just substitute all the x's in g(x) with whatever f(x)

Answer 2

shouldn't it be like... x substitute into g(x) = x^3 + x ^2?
im referring to a question that goes like this... g(f(-2))
u substitute -2 into x which i get -11
than substitute -11 into the g(x) to find 110

Answer 3

You have f(x)=2x-7 and g(x)=x^2+x
So, wherever you see an "x" you are going to replace it whenever you have a composite function. Before we step that far though, lets look at what you would do if you had g(1).
You would say: g(1)=(1)^2+1=2 right?
Well, the same thing works with functions, but instead of plugging in a number, you would plug in the entire FUNCTION wherever you see x. So if you want to do:
g(f(x)) you would plug in (2x-7) where you would have plugged in 1 in my previous example. So you would have g(f(x))=(2x-7)^2+(2x-7)
Does that make more sense?

Answer 4

so if it was f(g(x)), then you substitute all the x's in f(x) with what g(x) is

Answer 5

For further explanatory purposes, say they asked for f(g(x)). Then you would plug the entire function g(x) in for all "x"s in f(x). Giving:
f(g(x))=2(x^2+x)-7

Answer 6

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