Question

Please Help!
Consider the function. f (x) = 1/2x +1
a. Find the inverse of f(x) and name it g(x). Show and explain your work.
b. Use function composition to show that f(x) and g(x) are inverses of each other.
c. Draw the graphs of f(x) and g(x) on the same coordinate plane. Explain how your graph shows that the functions are inverses of each other.

Answer 1

please help i really need it

Answer 2

Why do you keep closing this question and opening a new one?
I was helping you.

Answer 3

You can do the next step after after what I told you in your previous thread. I will not type it over.

Answer 4

im sorry i just really need someone to help me get the answer fast

Answer 5

Well I think the point is for you to learn it? Learning isn't always a fast process.

Answer 6

yeah but i can't give you an answer if i don't know anything about it yet

Answer 7

That is why I was helping you. I'm gonna ask you questions. If you don't know the answer, you can just say you don't know and I will give you a clue just like I did in the previous thread you closed. You can look there to see what I asked you to do next.

Answer 8

ok sorry

Answer 9

You said y-1=x/2

Look at that x. It is being divided by 2. To undo division you multiply.
Since it is being divided by 2, you are going to multiply by 2.
Remember whatever you do to one side, you do to the other.
So if you multiply 2 on one side, you multiply 2 on the other.

Answer 10

ok so its y-2=x

Answer 11

Don't forget to muliply the y on the other side by 2.

So we have y-1=x/2
You multiply both sides by 2 we get
2(y-1)=2(x/2)

Distribute 2(y-1)
=2y - 2(1)
=2y - 2

So we have from doing *2 on both sides:
2y-2=x

or you can say it the other way around

x=2y-2

Now this in your inverse function.
\[\text{ Replace } x \text{ with } f^{(-1)}(x) \text{ and replace} y \text{ with } x\]

Answer 12

Like this:
x = 2 y - 2
\[f^{(-1)}(x)=2 x - 2\]

See that the x was replace with that f inverse thing and that y was replaced with x.

Answer 13

except they want you to name this function g(x) instead.

Answer 14

So what is g(x) equal to?

Answer 15

It is right there. All I want you to do is tell me what it is.

Answer 16

g(-1) (x) +2x -2 right??? :)

Answer 17

well they want you to just call it g(x)

Answer 18

g(x)=2x-2

Answer 19

Now they want you to prove they (f and g) are inverses of either other by simplifying f(g(x)) and g(f(x)).
Basically you are to show that both of these compositions are equal to x.

Answer 20

f(x)=x/2+1
g(x)=2x-2

To evaluate f(g(x)), plug your g function into f. Replace x with g(x) and g(x) is (2x-2).
So I'm asking you to do this
f(g(x))=g(x)/2+1
But g(x)=(2x-2)
So wherever you see g(x) put (2x-2)
like so:
f(2x-2)=(2x-2)/2+1
Now simplify.

Answer 21

ok to simplify do i subtract 1 from each side first? or do i cancel out (2x-2) on each side first?

Answer 22

You aren't doing something to both sides. You are working with one side
You are simplifying (2x-2)/2+1

Answer 23

There is a factor 2 in 2x and in 2
Because we can write 2x as 2*x
And we can write 2 as 2*1
They both have 2 in common.

So we can write (2x-2) as 2(x-1)

So we have (2x-2)/2 +1
is equal to 2(x-1)/2 + 1

Does anything cancel?

Answer 24

ok it would be (x)/3 or X/3 then right?

Answer 25

No the 2's cancel you are left with
(x-1)+1

Answer 26

If I wanted one to be apart of the denominator I would have said (2x-2)/(2+1).
(2x-2)/2 + 1 is not the same as that.

Answer 27

Remember f was x/2+1 not x/(2+1)

Answer 28

ok (x-1)+1 because i hav to cancel. ok! :) so far its making sense

Answer 29

That is x-1+1

Answer 30

You don't need parenthesis anymore.

Answer 31

-1+1 is zero so you are left with x.

Now you try doing g(f(x)).
After you have simplified you should get x.
If you don't, you made a mistake.

Answer 32

hahaha ok i got X!!!! All that leaves is question C. Can u show me how to graph them now?

Answer 33

y=x/2+1
y=2x-2
Both of these are linear equations.
They are both in the form y=mx+b
where m is slope and b is y-intercept

Graph the y-intercept and then use the slope to find another point (Connect the dots.)

Answer 34

ok thanks! you've helped me answer all my questions. Thanks and sorry about before.

Answer 35

It's cool. Have a good day. I'm glad you got it.

Answer 36

u too!!!!