Determine f(3) if f(3x)+3*f(-3x)=x+1

We'll create a new relation, substituting x by
-x.

f(-3x) + 3f(3x) = -x + 1
(2)

We'll put f(3x)+3*f(-3x)=x+1
(1)

We'll determine f(3x) from the system formed by the
relations (1) and (2):

f(-3x) = -x + 1 - 3*f(3x)
(3)

We'll substitute (3) in
(1):

f(3x) + 3[ -x + 1 - 3*f(3x)] = x +
1

We'll remove the
brackets:

f(3x) - 3x + 3 - 9f(3x) = x +
1

We'll combine like
terms:

-8f(3x) = 4x - 2

f(3x)
= -x/2 + 1/4

We'll substitute x by 1 and we'll get
f(3):

f(3) = -1/2 +
1/4

f(3) =
-1/4