Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 10 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal Choose the correct choice from the following choices:
A) 7
B) 9
C) 10
D) 11
E) 12

Rationale: since ( ii ) holds for every real number x , it will remain valid if we replace x with - x . therefore , f ( 1 - x ) = 3 + f ( - x ) . now , from ( i ) , 10 = f ( x ) + f ( 1 - x ) = f ( x ) + 3 + f ( - x ) so that f ( x ) + f ( - x ) = 10 - 3 = 7 . ( observe that f ( x ) = 3 x + 4 satisfies the conditions in the problem . ) correct answer a
Answer: A