Question

A simple functions one, :
A real valued function,f(x), satisfies the equation:
f(x - y) = f(x)f(y) - f(a-x)f(a+y) where a is a consant and f(0) = 1, Then f(2a-x) is?

Answer 1

You have to find it in terms of f(x).

Answer 2

is it -f(x)??

Answer 3

Yes.:)
Method?

Answer 4

put x=y
then put x=0, that will yield f(a) = 0
if we put, 2a-x as a - (x-a), we will get -f(x)

Answer 5

Ah ,,, putting x=y=0 would be shortcut

Answer 6

After x=y=0, f(a)=0
Put.x = a,
and y = a -x works as well.
However, the quickest way to do this is by comparing it to arc(cos(x-y))

Answer 7

arc(cos(x-y)) or arccos(x-y) ??

Answer 8

cos(inverse) (x-y)

Answer 9

Not used to the arc notation.

Answer 10

and a would be pi/2??

Answer 11

i see .. nice technique

Answer 12

Yeahhhhh. :)

Answer 13

-f(a-x)f(a+x) had me confused ... though i would have never guessed

Answer 14

Still. Nice way yours too! :)

Answer 15

:)