Question

3f(x-2)+f(2-x)=5x
f(x)=?

Answer 1

what class is this for?

Answer 2

Sorry I have no idea. @Callisto please tag me if you see this get solved.

Answer 3

\(x = 2\) gives \(3f(0) + f(0) = 10\implies f(0) = 5/2\)

differentiating we get \(f'(0) = 5/2\) and \(f^n(0) = 0\) for \(n\gt 2\)

so \(f(x) \) is a linear polynomial that passes through \((0, 5/2)\) with a slope of \(5/2\) :
\[f(x) = \frac{5}{2}x + \frac{5}{2}\]

Answer 4

why is f'(0) = 5/2?

Answer 5

3f(x-2)+f(2-x)=5x

differentiateing

3f'(x-2) - f'(2-x) = 5

plugin x=2

Answer 6

right

Answer 7

Very cool! nice work

Answer 8

works assuming f(x) is differentiable etc...

Answer 9

yeah, very clever