Relations and F...

If $$f(x + y) = f(xy)$$ and $$f(1) = 5$$, then the value of $$\sum_{k\, =\, 0}^{6}\, f(k)$$.  

R is a relation on set A then $$\displaystyle \left [ \left ( R^{-1} \right )^{-1} \right ]^{-1}$$ is_______

A relation which satisfies reflexive symmetric and transitive is ________ relation

If $$f(x) + f( 1- x) = 10$$, then the value of $$f\left ( \frac{1}{10} \right )\, +\, f\left ( \frac{2}{10} \right )\, +\, ..........\, +\, f\left ( \frac{9}{10} \right )$$ is

If $$\displaystyle f:R\rightarrow R$$ defined by $$\displaystyle f\left ( x \right )=2x^{2}-3x+5$$, then find the value of $$\displaystyle \frac{f\left ( x+h \right )-f\left ( x \right )}{h}$$ at $$\displaystyle h\neq 0$$

If $$\displaystyle R_{n}=\left \{ x:\frac{-1}{n}< x< \frac{1}{n} \right \}$$ then $$\displaystyle R_{5}\cup R_{15}=$$ ________

The domain of the function f(x) = $$\displaystyle \frac{\left | x \right |-2}{\left | x \right |-3}$$ is ________

An equation that defines $$y$$ as a function of $$x$$ is given. Solve for $$y$$ in terms of $$x$$, and replace $$y$$ with the function notation $$f\left( x \right)$$.
$$x - 2y = 18$$

$$A = \left \{1, 2, 3, 4\right \}$$ and $$B = \left \{a, b, c\right \}$$. The relations from $$A$$ to $$B$$ is

Find $$\left( f+g \right) \left( 1 \right) $$ when $$f\left( x \right) =x+6$$ and $$g\left( x \right) =x-3$$.