Algebra help! Inverse and composition functions

BlitzBall · 2012-01-18 02:38:51

bobbym wrote:

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)!

bobbym · 2012-01-18 02:43:55

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!

BlitzBall · 2012-01-18 02:48:06

bobbym wrote:

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!:)

bobbym · 2012-01-18 02:50:08

Okay, I am taking a little break for 20 minutes, I will see you then.

BlitzBall · 2012-01-18 02:50:51

Okay.

Last edited by BlitzBall (2012-01-18 02:51:30)

bobbym · 2012-01-18 03:24:30

Can you do another one?

BlitzBall · 2012-01-18 03:31:01

bobbym wrote:

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

bobbym · 2012-01-18 03:31:43

Hi;

Okay, then I will see you later. Let me know how you do.

BlitzBall · 2012-01-22 04:35:49

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) ???

bobbym · 2012-01-22 05:31:56

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

BlitzBall · 2012-01-22 05:41:26

bobbym wrote:

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?

bobbym · 2012-01-22 05:42:58

Hi;

I am not following you, what is y - 2/4 ?

BlitzBall · 2012-01-22 05:44:55

bobbym wrote:

Hi;
I am not following you, what is y - 2/4 ?

Ohhh I forgot. I meant inversing y-2/4.

bobbym · 2012-01-22 05:47:50

Hi;

You need another variable. Are we talking about x = y - 2 / 4 ?

BlitzBall · 2012-01-22 05:56:17

bobbym wrote:

Hi;
You need another variable. Are we talking about x = y - 2 / 4 ?

Yes yes. I forgot that:|

bobbym · 2012-01-22 06:01:04

Times both sides by 4.

Are you okay up to here?

BlitzBall · 2012-01-22 06:04:09

Yup

bobbym · 2012-01-22 06:06:02

The left side becomes 4x, on the right side the four on top cancels the one on the bottom and we are left with this:

Okay?

BlitzBall · 2012-01-22 06:08:22

Yep. I understood that

bobbym · 2012-01-22 06:10:51

We are trying to get the y by itself. If that -2 were gone we would have it all alone. The inverse operation to subtraction is addition. So we add 2 to both sides.

Okay, up to here?

BlitzBall · 2012-01-22 06:13:27

Yes. but wouldn't the +2 on the left hand-side be 2 + 4x ??

bobbym · 2012-01-22 06:14:44

Yes, but addition does not care what goes first. 1 + 3 is the same as 3 + 1. So 2 + 4x is the same as 4x + 2.

BlitzBall · 2012-01-22 06:18:15

Oh right i get that.

bobbym · 2012-01-22 06:20:55

We are up to here:

On the right side we see that we are subtracting 2 and adding 2. This equals 0, so the -2 + 2 equals 0. That leaves us:

We are close!

BlitzBall · 2012-01-22 06:30:00

Yep I got that.

Math Is Fun Forum

#51 2012-01-18 02:38:51

Re: Algebra help! Inverse and composition functions

#52 2012-01-18 02:43:55

Re: Algebra help! Inverse and composition functions

#53 2012-01-18 02:48:06

Re: Algebra help! Inverse and composition functions

#54 2012-01-18 02:50:08

Re: Algebra help! Inverse and composition functions

#55 2012-01-18 02:50:51

Re: Algebra help! Inverse and composition functions

#56 2012-01-18 03:24:30

Re: Algebra help! Inverse and composition functions

#57 2012-01-18 03:31:01

Re: Algebra help! Inverse and composition functions

#58 2012-01-18 03:31:43

Re: Algebra help! Inverse and composition functions

#59 2012-01-22 04:35:49

Re: Algebra help! Inverse and composition functions

#60 2012-01-22 05:31:56

Re: Algebra help! Inverse and composition functions

#61 2012-01-22 05:41:26

Re: Algebra help! Inverse and composition functions

#62 2012-01-22 05:42:58

Re: Algebra help! Inverse and composition functions

#63 2012-01-22 05:44:55

Re: Algebra help! Inverse and composition functions

#64 2012-01-22 05:47:50

Re: Algebra help! Inverse and composition functions

#65 2012-01-22 05:56:17

Re: Algebra help! Inverse and composition functions

#66 2012-01-22 06:01:04

Re: Algebra help! Inverse and composition functions

#67 2012-01-22 06:04:09

Re: Algebra help! Inverse and composition functions

#68 2012-01-22 06:06:02

Re: Algebra help! Inverse and composition functions

#69 2012-01-22 06:08:22

Re: Algebra help! Inverse and composition functions

#70 2012-01-22 06:10:51

Re: Algebra help! Inverse and composition functions

#71 2012-01-22 06:13:27

Re: Algebra help! Inverse and composition functions

#72 2012-01-22 06:14:44

Re: Algebra help! Inverse and composition functions

#73 2012-01-22 06:18:15

Re: Algebra help! Inverse and composition functions

#74 2012-01-22 06:20:55

Re: Algebra help! Inverse and composition functions

#75 2012-01-22 06:30:00

Re: Algebra help! Inverse and composition functions

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