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Yes. but wouldn't the +2 on the left hand-side be 2 + 4x ??
Yep. I understood that
Hi;
You need another variable. Are we talking about x = y - 2 / 4 ?
Yes yes. I forgot that:|
Hi;
I am not following you, what is y - 2/4 ?
Ohhh I forgot. I meant inversing y-2/4.
Hi
For g and g... I get (x+8)+8. In this situation, would you have to multiply both 8's or add them
You did the composition correctly, now you add the eights.
For the second question:
3x+ 2 is not the same as 3(x+2). 3(x+2) means multiply everything in the parentheses by 3. So you get:
3x + 3(2) = 3x + 6
Hmm... I see. Heres an example, y-2/4, I get 4(x+2), but the answer is 4x+2.
Am I missing something?
I'm back. Great news! I think I understand this! However, I have a few problems that I want to clear up on. In the composition functions, Say you have f(x) = 2x and g(x) = x+8.
For g and g... I get (x+8)+8. In this situation, would you have to multiply both 8's or add them?
Also, for inverse function. Is 3x+2 the same as 3(x+2) ???
Can you do another one?
I will do another for myself and see how I will go. I have to study for another module. So, for now, you can relax ![]()
Okay.
Now use some algebra to clean that up a little.
f(x+1) = x+1 + 4
Simplifying often just means combining things together. Well the 1 + 4 is 5 so that means we can simplify that to.
f(x+1) = x+5
We are done!
Ahh I get it now! YESS!:)
HI;
f(g(x)) = g(x) + 4
Now we replace that g(x) with x + 1 because g(x) = x + 1.
f(x+1) = x+1 + 4
See how each g(x) was replaced by a x+1?
Yes. the x from f(x) is replaced with the equation of g(x)!
Hi;
Hold it, watch what I am doing.
f(g(x)) = g(x) + 4
See the boldfaced g(x) in the above equation?
OOh yeaah. I forgot to put that on. oops.
Okay. f(x) = g(x) + 4 ? Or is it the wrong way round?
Hi;
You skipped a step.
f(x) = x + 4
Now putting a g(x) wherever we have a x in f(x) we get:
f(g(x)) = g(x) + 4
Ohhh I get that. In that step you just plot g(x) in x from f(x).
Hi;
Not quite. But do not get discouraged you will soon do it like a champion.
See the x in the equation
f(x) = x + 4? I want you to put a g(x) wherever you see one.
Hmmm. Putting g(x) will result in x(x+1)+4 ?
Okay, I will put another one down and you do it for me:
What is?
(x^2+1)+4 ??
Hi;
Not exactly, all we are doing is substituting. Then we have some algebra to clean it up.
Let's do another one:
Wherever the is an x , we substitue g(x) for it and g(x) = 2x.
Ohhh okay. I think I get that. I was wondering why do we need the brackets?
Hi;
f(x)=2x+3
g(x) = x+3
This just means:
So for every x in f(x) we substitue a g(x)
Follow up to here?
I think I get it. When there is x in f(x) and g(x), it can't be turned into x^2.
Hi;
I meant in particular.
Like getting putting g into f and f into g. I get mixed up on which way to input correctly.
Okay, what problems are you working on, I forgot.
The composition of functions.
Hi BlitzBall;
Well rested and ready to go!
Hi, I'm ready to go ![]()
Hi;
You would first minus 6 from both sides and then divide by 4 to both sides.
It is time to sleep for a couple of hours, I am really tired. I will see you later and help with the compositions if no one else has
Oh right I will give it a try. Thank you, Bob. Good Night![]()
One more step:
And we are done!
Ahhh I get it. Last quick question, what if it was 4x + 6? Wouldn't that be the same method as you showed me?? Just explain it. I don't want to waste a lot of your time.
x/ 4 is the same as x * ( 1 / 4 ). The fours cancel in either case and just leave the x.
Now we swap the x to the other side.
Ohh I see. Surely, that is the answer??
No, it would be one, because 4 * ( 1 / 4 ) = 1. So let's clean up this last step.
Okay. So, doing *4 on the right-side leaves x on its own, and the fraction is removed? where is 1/4 coming from?