SOLUTION: I am not looking for any particular homework help, I would just like to get g(f(x)) explained to me. I don;t understand anything about it.

Question 105814: I am not looking for any particular homework help, I would just like to get g(f(x)) explained to me. I don;t understand anything about it.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
If you are given two functions ... one of them f(x) and the other g(x) all that it means if
you are asked to find g(f(x)) is to go to g(x) and for every x you find in it, substitute
f(x).
.
As an example. Suppose you are given:
.
f(x) = 2x - 1 and
g(x) = x^2 - 2x + 3
.
To find g(f(x)) means start with g(x) and in place of the x in the terms it contains,
substitute the right side of the equation for f(x).
.
Start with:
.
g(x) = x^2 - 2x + 3
.
In place of each of the x's in g(x) substitute 2x - 1 to get g(f(x))
.
g(f(x)) = (2x-1)^2 - 2(2x - 1) + 3
.
Look carefully at this ... see how the x's in g(x) have been replaced by 2x -1 which is f(x).
.
Now all you have to do is the math. Square out (2x - 1) to get 4x^2 - 4x + 1 and multiply
-2 times (2x - 1) to get -4x + 2
.
Substitute these multiplications to get:
.
g(f(x)) = 4x^2 - 4x + 1 - 4x + 2 + 3
.
On the right side combine the -4x and the -4x to get -8x and combine the +1 with the +2 and
the +3 to get +6. Insert these results and the equation for g(f(x)) becomes:
.
g(f(x)) = 4x^2 - 8x + 6
.
Hopefully this example makes sense to you and you can see how g(f(x)) is found when you
are given both g(x) and f(x).
.
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