QR question

[drteeth]

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If f(x)=x, the inverse of f, f^-1, could be represented by?

The answer given is f^-1(x) = x

I thought it would be f^-1(x) = y???

Anyone know how this answer was obtained. Its a Barrons question, and we all know about Barrons, so Im thinking they could be wrong?

 

[Ocean5]

If f(x)=x, the inverse of f, f^-1, could be represented by?

The answer given is f^-1(x) = x

I thought it would be f^-1(x) = y???

Anyone know how this answer was obtained. Its a Barrons question, and we all know about Barrons, so Im thinking they could be wrong?

May I ask where is this qs?

 

[drteeth]

Its actually from an SAT II math book....

 

[z3u2]

it's correct
but i don't have time to explain this now, maybe later today or somebody else can.

 

[Streetwolf]

I don't know where you got a 'y' from. The original equation says f(x) = x. So if the function takes x to x, the inverse takes x back to x. It confuses you because they are the same variable. If instead it said take the inverse of f(x) = x' (read x-prime), then the answer would be f^-1(x') = x.

 

[z3u2]

another way to explain this, if u want to see it visually.

draw out the graph on a piece of a paper, rotate the paper in such a way that you can see it's inverse graph, u'll see the graph looks exactly the same.


if u don't know what it means to rorate the paper here's how: hold it up.
flip the paper over (flip from the up-down direction)
then rotate the paper counter clock-wise by 90 degrees.

it works on EVERY function graphs
-----
yet another way
let y = f(x)
y = x
to find the inverse, you swap x variable with y variable, and y variable with x variable:
x = y

you can see it's still the same graph

 

[drteeth]

aaaaah got it! I was looking at incorrectly....

Thanks for the help kids!

ps - QR = pain in my arse!!!!!