An odd function is symmetric about the vertical line `x=a ,(a >0),a n dif` `sum_(r=0)^oo[f(1+4r]^r=8,` then find the value of `f(1)dot`

If f(x+f(y))=f(x)+yAAx ,y in R a n df(0)=1, then find the value of f(7)dot

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

If f(x)=4x-x^2, x in R , then write the value of f(a+1)-f(a-1)dot

Let f(n)=sum_(r=0)^nsum_(k=r)^n(k r)dot Find the total number of divisors of f(9)dot

Consider a twice differentiable function f(x) of degree four symmetrical to line x = 1 defined as f: R rarr R and f''(2) = 0. if f(1)=0, f(2)=1 then the value of f(3) is

If A=pi/5, then find the value of sum_(r=1)^8tan(r A)*tan((r+1)A)dot

If A=pi/5, then find the value of sum_(r=1)^8tan(r A)tan((r+1)A)dot

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

f(x)+f(1-1/x)=1+x for x in R-{0,1}. Find the value of 4f(2).

If f(x)=(a^x)/(a^x+sqrt(a ,)),(a >0), then find the value of sum_(r=1)^(2n1)2f(r/(2n))