Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 14 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal
Choose the correct choice from the following choices: 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), 14 = f(x)+f(1-x) = f(x)+3+f(-x)   so that f(x) + f(-x) = 14-3= 
<gadget id="calculator">14-3</gadget>
<output>11</output>
11. (Observe that f(x)= 3x + 4 satisfies the conditions   in the problem.)   correct answer 11
<result>D</result>
Suppose that f(x) is a function such that for every real number x,i)f(x)+f(1-x) = 14 and (ii) f(1+x) = 3+f(x). Then f(x)+f(-x)
must equal