If f(x) + f(1 - x) + f(1 + x) + f(2 + x) = 2x for all real value of x. If f(0) = 1, then find the value of f(4)  Select the correct option:  A) 1  B) 2  C) 8  D) 7  E) 9
For x = 0, f(0) + f(1) + f(2) = 0 ............. (i)   For x = 1, f(1) + f(0) + f(3) = 2 ............. (ii)   subtracting (i) from (ii), we get f(3) - f(1) = 2 .......... (a)   For x (3) -  (1)= 
<gadget id="calculator">(3) -  (1)</gadget>
<output>2</output>
2 .......... (a)   For x= 2, f(2) + f(-1) + f(3) + f(4) = 4 ........ (iii)   For x = -1, f(-1) + f(2) + f(0) + f(1) = -2 ......... (iv)   subtracting from (iii) from (iv), we get   ⇒f(0)−f(4)−2=−6⇒f(0)−f(4)−2=−6 [ from (a) we know that f(3) - f(1) = 2]   Answer:2(3) -  (1)= 
<gadget id="calculator">(3) -  (1)</gadget>
<output>2</output>
2]   Answer:2
<result>B</result>
If f(x) + f(1 - x) + f(1 + x) + f(2 + x) = 2x for all real value of x. If f(0) = 1, then find the value of f(4)