Algebra help! Inverse and composition functions

bobbym · 2012-01-17 11:52:01

One more step:

And we are done!

BlitzBall · 2012-01-17 11:57:34

bobbym wrote:

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.

Last edited by BlitzBall (2012-01-17 11:57:59)

bobbym · 2012-01-17 11:58:52

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

BlitzBall · 2012-01-17 12:01:30

bobbym wrote:

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

bobbym · 2012-01-17 22:50:50

Hi BlitzBall;

Well rested and ready to go!

BlitzBall · 2012-01-18 01:19:24

bobbym wrote:

Hi BlitzBall;
Well rested and ready to go!

Hi, I'm ready to go

bobbym · 2012-01-18 01:21:25

Okay, what problems are you working on, I forgot.

BlitzBall · 2012-01-18 01:22:42

bobbym wrote:

Okay, what problems are you working on, I forgot.

The composition of functions.

bobbym · 2012-01-18 01:25:40

Hi;

I meant in particular.

BlitzBall · 2012-01-18 01:29:27

bobbym wrote:

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.

bobbym · 2012-01-18 01:40:22

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?

BlitzBall · 2012-01-18 01:45:55

bobbym wrote:

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.

bobbym · 2012-01-18 01:50:09

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.

BlitzBall · 2012-01-18 01:55:53

bobbym wrote:

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?

Last edited by BlitzBall (2012-01-18 01:57:22)

bobbym · 2012-01-18 01:57:56

Okay, I will put another one down and you do it for me:

What is?

BlitzBall · 2012-01-18 02:02:22

bobbym wrote:

Okay, I will put another one down and you do it for me:
What is?

(x^2+1)+4 ??

bobbym · 2012-01-18 02:06:25

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.

BlitzBall · 2012-01-18 02:13:07

bobbym wrote:

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 ?

bobbym · 2012-01-18 02:15:30

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

BlitzBall · 2012-01-18 02:18:45

bobbym wrote:

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).

bobbym · 2012-01-18 02:23:03

Yes, you replace every x with a g(x), now you have:

f(g(x)) = g(x) + 4

Now from post #40 we have g(x) = x + 1. Now take and change each g(x) into x + 1.

BlitzBall · 2012-01-18 02:29:38

Okay. f(x) = g(x) + 4 ? Or is it the wrong way round?

bobbym · 2012-01-18 02:32:07

Hi;

Hold it, watch what I am doing.

f(g(x)) = g(x) + 4

See the boldfaced g(x) in the above equation?

BlitzBall · 2012-01-18 02:33:58

bobbym wrote:

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.

bobbym · 2012-01-18 02:36:39

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?

Math Is Fun Forum

#26 2012-01-17 11:52:01

Re: Algebra help! Inverse and composition functions

#27 2012-01-17 11:57:34

Re: Algebra help! Inverse and composition functions

#28 2012-01-17 11:58:52

Re: Algebra help! Inverse and composition functions

#29 2012-01-17 12:01:30

Re: Algebra help! Inverse and composition functions

#30 2012-01-17 22:50:50

Re: Algebra help! Inverse and composition functions

#31 2012-01-18 01:19:24

Re: Algebra help! Inverse and composition functions

#32 2012-01-18 01:21:25

Re: Algebra help! Inverse and composition functions

#33 2012-01-18 01:22:42

Re: Algebra help! Inverse and composition functions

#34 2012-01-18 01:25:40

Re: Algebra help! Inverse and composition functions

#35 2012-01-18 01:29:27

Re: Algebra help! Inverse and composition functions

#36 2012-01-18 01:40:22

Re: Algebra help! Inverse and composition functions

#37 2012-01-18 01:45:55

Re: Algebra help! Inverse and composition functions

#38 2012-01-18 01:50:09

Re: Algebra help! Inverse and composition functions

#39 2012-01-18 01:55:53

Re: Algebra help! Inverse and composition functions

#40 2012-01-18 01:57:56

Re: Algebra help! Inverse and composition functions

#41 2012-01-18 02:02:22

Re: Algebra help! Inverse and composition functions

#42 2012-01-18 02:06:25

Re: Algebra help! Inverse and composition functions

#43 2012-01-18 02:13:07

Re: Algebra help! Inverse and composition functions

#44 2012-01-18 02:15:30

Re: Algebra help! Inverse and composition functions

#45 2012-01-18 02:18:45

Re: Algebra help! Inverse and composition functions

#46 2012-01-18 02:23:03

Re: Algebra help! Inverse and composition functions

#47 2012-01-18 02:29:38

Re: Algebra help! Inverse and composition functions

#48 2012-01-18 02:32:07

Re: Algebra help! Inverse and composition functions

#49 2012-01-18 02:33:58

Re: Algebra help! Inverse and composition functions

#50 2012-01-18 02:36:39

Re: Algebra help! Inverse and composition functions

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