Given the function $f(x) = \frac{a^x + a^{-x}}{2}, (a > 2)$,then $f(x + y) + f(x - y)$ is equal to

If a function $f$ satisfies $f(x+1)+f(x-1)=\sqrt{2} f(x)$,then $f(x+2)+f(x-2)=$

Let $R$ be the set of all real numbers and let $f$ be a function from $R$ to $R$ such that $f(x) + (x + \frac{1}{2}) f(1 - x) = 1$,for all $x \in R$. Then $2 f(0) + 3 f(1)$ is equal to

If $f: R \rightarrow R$ is defined by $f(x+y)=f(x)+f(y)$ for all $x, y \in R$ and $f(1)=7$,then $\sum_{r=1}^n f(r)=$

Let $f: R \rightarrow R$ be a function defined by $f(x)=(2+3a)x^2 + \left(\frac{a+2}{a-1}\right)x + b$,where $a \neq 1$. If $f(x+y) = f(x) + f(y) + 1 - \frac{2}{7}xy$,then the value of $28 \sum_{i=1}^3 |f(i)|$ is:

If $f: R \rightarrow R$ is defined as $f(x+y)=f(x)+f(y), \forall x, y \in R$ and $f(1)=10$, then, $\sum_{r=1}^n(f(r))^2=$