f(x) is a function such that f(x) + 3f(8 - x) = x for all real numbers x. Find the value of f(2).
Pick one.
A) 5 B) 4 C) 3 D) 2 E) 1

Rationale: f ( x ) + 3 f ( 8 - x ) = x : given f ( 2 ) + 3 f ( 6 ) = 2 : x = 2 above f ( 6 ) + 3 f ( 2 ) = 6 : x = 6 above f ( 6 ) = 6 - 3 f ( 2 ) : solve equation c for f ( 6 ) f ( 2 ) + 3 ( 6 - 3 f ( 2 ) ) = 2 : substitute f ( 2 ) = 2 : solve above equation . correct answer is d ) 2
Answer: D