Silly Questions Thread

[Blakhitman]

AND

[the.watchman]

AND

Yep, oops...

[Blakhitman]

LOL,

And I would have expanded the first one, because it's easier to see similarities than having to factorise the second one. Personal preference!

[Aqualim]

ahh cheers how about this one;
Write a matrix equation that would complete the transformations on (x,y) to (x',y') with the function

[the.watchman]

You mean from ?

Then it'd be:

[x'  = [0.5  0 [x  + [-0.5
 y']     0    1] y]       0  ]

Because, in this scenario,

Then

[Aqualim]

Yeah that was I got, but will it be the same if you sub it into ?

[Aqualim]

ok this is a follow-up question to the above;

The inverse of a function, , is the reflection of a function in the line y=x, which can be found by pre-multiplying the matrix . Using matrix operations show that f(x) and g(x) are inverse functions. ().

Ok so in the previous question I found that the inverse of f(x) was , therefore I'm assuming the question is wanting me to be able to do this through matrix operations. How would I do that?

[brightsky]

Hmm...don't really get the question. So it's asking you to prove is the inverse of ?

[Aqualim]

thats what I'm wondering aswell, How can I show two functions as inverses? I'll post up the entire question so you can get a better understanding of the previous questions.

[brightsky]

But f(x) is clearly not an inverse of g(x) and vice versa.

The inverse of y = f(x) is, as you've found:



You can prove this the other way around as well:

The inverse of y = g(x) is .

EDIT: Hmm..really think I'm missing something here...xD

[Blakhitman]

and in general if two functions f(x) and g(x) are inverses of each other, then and

[Aqualim]

But f(x) is clearly not an inverse of g(x) and vice versa.

The inverse of y = f(x) is, as you've found:



You can prove this the other way around as well:

The inverse of y = g(x) is .

EDIT: Hmm..really think I'm missing something here...xD

Yeah I think it's a badly worded question, not really 100% sure what it is asking of me

[Blakhitman]

I don't think it's asking to show they're inverses of "each other". Just show that they are inverse functions.

For example, is known to be the inverse of so simply show that through the matrix operation.

[Aqualim]

I don't think it's asking to show they're inverses of "each other". Just show that they are inverse functions.

For example, is known to be the inverse of so simply show that through the matrix operation.

Ok how would I do that exactly? is there a formula for inverses in matrices?

[Blakhitman]

You posted it before .



you get and then sub in (note it's the swapping x and y business) to and you get

Then do same for f(x) lol