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

Explanation

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)`

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