Consider the function f(x)=12x+2.f(x)=12x+2. Find the value of 2[f(5)+f(4)+f(3)+f(2)+f(1)+f(0)+f(1)+f(2)+f(3)+f(4)+f(5)+f(6)].


Answer:

6

Step by Step Explanation:
  1. Given, f(x)=12x+2
    Here, f(5) can be written asf(16).
    Similarly, f(4)=f(15),f(3)=f(14),        f(0)=f(11)
  2. We have
    f(x)=12x+2f(1x)=121x+2f(x)+f(1x)=12x+2+121x+2f(x)+f(1x)=22(2x+2)+2x2x(21x+2)f(x)+f(1x)=22x2+2+2x2+2x2f(x)+f(1x)=2+2x2+2x2f(x)+f(1x)=2+2x2(2+2x)f(x)+f(1x)=12
  3. Now,
    2[f(5)+f(4)+f(3)+f(2)+f(1)+f(0)+f(1)+f(2)+f(3)+f(4)+f(5)+f(6)]2[{f(6)+f(16)}+{f(5)+f(15)}++{f(2)+f(12)}+{f(1)+f(11)}]2[62]6
  4. Hence, the value of the given expression is 6.

You can reuse this answer
Creative Commons License