Algebra help! Inverse and composition functions

bobbym · 2012-01-22 06:36:26

Now we just switch them around.

We are done!

BlitzBall · 2012-01-22 06:47:32

Ohhh I got it now. Going to do more practice on these! Thank you

bobbym · 2012-01-22 06:49:51

Hi BlitzBall;

Your welcome! See you then.

I am going to get something to eat.

BlitzBall · 2012-01-23 07:04:13

Sorry to ask you again But I have a small problem. It's a little off topic, but how would you answer this question...

The function f : A to B is given by f(x) = 1+ 2/x, where A denotes the set of
real numbers excluding 0 and B denotes the set of real numbers excluding 1.
Show that f is bijective and determine the inverse function.

I don't understand this question. Can anyone explain it to me?

bobbym · 2012-01-23 07:07:33

To show that it is bijective you must prove that it is injective and surjective.

The inverse you already know how to do because we did a lot of them together. Do you need more review here?

BlitzBall · 2012-01-23 07:25:29

Hmmm you are right. I looked at the answer, an it says 'If f(x) = y, then 1+2/x = y and so x= 2/(y-1)'. I was wondering, where has the 2/(y-1) come from :S How did it get there??

bobbym · 2012-01-23 07:26:24

Did you try to solve for x as we have been doing?

That is how it got there. A little tricky! Want to go over it?

BlitzBall · 2012-01-23 07:40:30

Yes.. but it looks different

bobbym · 2012-01-23 07:43:25

Did you see what I did in the post before yours?

BlitzBall · 2012-01-23 07:51:54

I didn't get what happens after y-1 = 2/x. Can you explain how you got x(y-1)=2 ??

bobbym · 2012-01-23 07:56:06

What you do to go from line 2 to line 3 is to multiply both sides by x.

BlitzBall · 2012-01-23 07:58:58

Oh right! However, Why are you multiplying x, but not 2 ??

bobbym · 2012-01-23 08:02:51

Because the x is on the bottom which means it is dividing into 2. To get it over to the other side we multiply by x.

The x's will cancel out on the right.

BlitzBall · 2012-01-23 08:06:40

Ohhhhh! Silly me. From line 3 to 4, I got (y-1)/2, but your's the opposite round.

bobbym · 2012-01-23 08:07:27

Did you see what I did in post #88?

BlitzBall · 2012-01-23 08:15:08

Ohh. You replaced the x that was above 2/ , and input (y-1) instead ?? That the right way of doing it??

bobbym · 2012-01-23 08:18:19

Watch what I am doing.

We multiply both sides by x.

The x's will cancel out on the right.

BlitzBall · 2012-01-23 08:29:15

Okay. In 2/x, the x is just replaced by the (y-1) ??

bobbym · 2012-01-23 08:32:27

Hi;

Think of it this way. We had this and I multiplied both sides by x

to get this.

BlitzBall · 2012-01-23 08:41:11

Yes I get that. /you multiply both sides.

bobbym · 2012-01-23 08:46:13

The left side stays the same but on the right we see an x on the bottom and an x on top. These can cancel ( be crossed out ) to make a 1.

See how the two x's are crossed out?

BlitzBall · 2012-01-23 08:54:13

Yep.

bobbym · 2012-01-23 08:55:45

What you are left with is this

The one comes from the cancelling of the x's.

BlitzBall · 2012-01-23 09:00:21

Ah ok. I was wondering does x count as 1 ?

bobbym · 2012-01-23 09:02:00

Nope, x is a variable. It stands for a number but we do not know what that number is.

Math Is Fun Forum

#76 2012-01-22 06:36:26

Re: Algebra help! Inverse and composition functions

#77 2012-01-22 06:47:32

Re: Algebra help! Inverse and composition functions

#78 2012-01-22 06:49:51

Re: Algebra help! Inverse and composition functions

#79 2012-01-23 07:04:13

Re: Algebra help! Inverse and composition functions

#80 2012-01-23 07:07:33

Re: Algebra help! Inverse and composition functions

#81 2012-01-23 07:25:29

Re: Algebra help! Inverse and composition functions

#82 2012-01-23 07:26:24

Re: Algebra help! Inverse and composition functions

#83 2012-01-23 07:40:30

Re: Algebra help! Inverse and composition functions

#84 2012-01-23 07:43:25

Re: Algebra help! Inverse and composition functions

#85 2012-01-23 07:51:54

Re: Algebra help! Inverse and composition functions

#86 2012-01-23 07:56:06

Re: Algebra help! Inverse and composition functions

#87 2012-01-23 07:58:58

Re: Algebra help! Inverse and composition functions

#88 2012-01-23 08:02:51

Re: Algebra help! Inverse and composition functions

#89 2012-01-23 08:06:40

Re: Algebra help! Inverse and composition functions

#90 2012-01-23 08:07:27

Re: Algebra help! Inverse and composition functions

#91 2012-01-23 08:15:08

Re: Algebra help! Inverse and composition functions

#92 2012-01-23 08:18:19

Re: Algebra help! Inverse and composition functions

#93 2012-01-23 08:29:15

Re: Algebra help! Inverse and composition functions

#94 2012-01-23 08:32:27

Re: Algebra help! Inverse and composition functions

#95 2012-01-23 08:41:11

Re: Algebra help! Inverse and composition functions

#96 2012-01-23 08:46:13

Re: Algebra help! Inverse and composition functions

#97 2012-01-23 08:54:13

Re: Algebra help! Inverse and composition functions

#98 2012-01-23 08:55:45

Re: Algebra help! Inverse and composition functions

#99 2012-01-23 09:00:21

Re: Algebra help! Inverse and composition functions

#100 2012-01-23 09:02:00

Re: Algebra help! Inverse and composition functions

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