Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 15 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
Choose the correct option
A) 8
B) 9
C) 10
D) 11
E) 12
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), 15 = f(x)+f(1-x) = f(x)+3+f(-x)   so that f(x) + f(-x) = 15-3= 
<gadget id="calculator">15-3</gadget>
<output>12</output>
12. (Observe that f(x)= 3x + 4 satisfies the conditions   in the problem.)   correct answer 12
<result>E</result>
Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 15 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal