Expert: Ahmed Salami - 8/13/2004

Question
solve this function:
5f(x)+3f(-x)=x6

note: x6=x^6  eg(2^6=2x2x2x2x2x2)
thank you


Answer
Hi mojtaba,
Well, there are quite a number of ways to look at it. But let's try this.
Let both sides of the equation be equal to a function g(x), we now have
g(x)= 5f(x) + 3f(-x)= x^6
Now,
g(-x)= 5f(-x) + 3f(x)= (-x)^6
but (-x)^6 = x^6, so
g(-x)= 5f(-x) + 3f(x)= x^6
Comparing the first and third equations, we have
5f(x) + 3f(-x)= 5f(-x) + 3f(x)
which gives f(x)= f(-x)
Introducing back into the first equation gives
8f(x)= x^6
f(x)= (x^6)/8
I hope you understand this.
You can always get back to me.
Regards.