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If the graph of non-constant function is symmetric about the point (3,4), then the value of `sum_(r = 0)^6 f(r) + f(3)` is equal to |
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Answer» Here, we are given, `f(3) = 4` As, given function is symmetric. `:. f(3+h) = 3+k` `f(3-h) = 3-k` Here, `h` and `k` are constants. Now, `sum_(r=0)^6f(r) +f(3) = f(0)+f(1)+f(2)+f(3)+f(4)+f(5)+f(6)+f(3)` `=2f(3)+f(1)+f(5)+f(2)+f(4)+f(0)+f(6)` `=2f(3)+f(3-2)+f(3+a)+f(3-1)+f(3+1)+f(3-3)+f(3+3)` From the property of symmetric functions, `=2(4)+4-a+4+a+4-b+4+b+4-c+4+c` (`a,b,c` are constants.) ` = 8+8+8+8 =32` `:.` Value of given expression will be `32`. |
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