Inverse Function Question Help. (1 Viewer)

[AirbusA380]

Hey guys, just need some help finding the inverse of a function for a holiday assignment. The function is x^2+4x-5 and the question asks to find the inverse of the graph (the equation). The inverse that i found im not sure is right. Thanks.

 

[photastic]

This is what I got

 

[AirbusA380]

This is what I got

I managed to find how to do it by switching x and y and i ended up getting y=(sqroot of x+9) +2, but instead i used the completing the square method. But even with yours, the next question says gives two restrictions to the domain that makes the inverse a function? For it to be a function you can do the vertical line test, but i couldnt think of anything that would change the domain but only that could change the range to make it a function? Even if yours is correct, what could be the possible domain restrictions. Thanks for your help.

 

[SpiralFlex]

Edit: I read as inverse function, which you cannot find in this case but an inverse relation you can.

 

[AirbusA380]

Ok, that makes sense. I managed to somehow (previsouly in holidays) to get the same restrictions. However, when i did the inverse i managed to get y= sqroot (x+9) +2. is this correct? I used the completing the square method. Or do you have to find the inverse for each restricted function?

 

[SpiralFlex]

Yes that is correct AirBus.

The above poster accidentally added a 2 instead of a 4.

 

[AirbusA380]

So for a i got x^2 + 4x - 5
and b) i drew it.
c) i got an inverse of sqroot (x+9) +2. (But this is for the entire function, not the two restricted original function.
d) i got the same as above.
e) (x+9)^0.5 -2
and f) ive alreayd worked out.

 

[AirbusA380]

Yes that is correct AirBus.

The above poster accidentally added a 2 instead of a 4.

Thanks mate. The explanation helped so much!

 

[AirbusA380]

So to be a pain. Last question.

In particular part c.
for a i drew the original and for b) i did the same and got f^-1(x)=(x+4)/3

 

[SpiralFlex]

 

[SpiralFlex]

Also I don't recall inverse function topic to be in 2U...

For question c) you have

Graph that!

What is the effect of having ?

 

[AirbusA380]

Sweet, thats all good now. Can you help me with the reply (qoute) above?

 

[AirbusA380]

Also I don't recall inverse function topic to be in 2U...

For question c) you have

Graph that!

What is the effect of having ?

So for b) (the inverse) i got (x+4)/3 which as far as im aware is the same as 1/3(x+4). I can remember seeing that |f^-1(x)| around in a topic but can remember its effect or what it means. If i graph both on my CAS there the same.

 

[AirbusA380]

Wait, I think i got it. Its the absolute function. (|x+4|)/3

 

[SpiralFlex]

So for b) (the inverse) i got (x+4)/3 which as far as im aware is the same as 1/3(x+4). I can remember seeing that |f^-1(x)| around in a topic but can remember its effect or what it means. If i graph both on my CAS there the same.

They are in fact NOT the same!

 

[aDimitri]

yeah you're right spiral, inverse functions isn't in 2U.

 

[AirbusA380]

They are in fact NOT the same!

Well then what does it equal. If |f^-1(x)| is only going to contain a positive value and x = either (x+4)/3 or 1/3(x+4)? And how do i know which one is correct (x+4)/3 or 1/3(x+4)? Totally confused now. But i do remeber absoolute value and the y=|x|. Even if x is a ngeative value, in |x| it is always positive.