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[Lukybear]

I guess this is sort of 3 unit stuff.

Two questiions

Given that f(x) is odd and has an inverse which is also a functio, show that f^-1(x) is also odd.


Second

Given any function f(x), define g(x) = 1/2 (f(x) + f(-x)) and h(x) = 1/2(f(x)-f(-x))

 

[Cazic]

Since f has an inverse, we have:



Did you finish off the last part of your question?

 

[Cazic]

Ok, taking a guess at what your second question was supposed to ask:



So g is even. You ok to show the second one is odd now?

 

[Lukybear]

Well thats the question and you guessed it. But is it really like that. Cause it said define g(x) as.... and i was assuming a little more algebra.

 

[Lukybear]

Ok, taking a guess at what your second question was supposed to ask:



So g is even. You ok to show the second one is odd now?

Did you figure this out yourself or was it taught at school or smthing?

 

[Cazic]

Well, how is f^-1 defined?



Now just take y = f(x) to see that f^-1(f(x)) = x.

Edit: Doh, you changed your questions Well I'll leave it there in case it helps anyone else.

As for your new question, I'm not sure what you mean?