Relations and F...

If $$k\ \epsilon\ R^+$$ and the middle term of $$(\dfrac{k}{2} + 2)^8$$ is $$1120$$, then value of k is

If $$f(x)=\sin^{2}x+x\sin 2x.\log x$$ then $$f(x)=0$$ has:

$$f(n) = \begin{cases} e^{-y_2}, n \neq 0 & f'(0) = ?\\ 0, n = 0\end{cases}$$

If $$f\left(x\right)=\dfrac{x}{x-1}$$, then $$\dfrac{ f\left(a\right)}{ f\left(a+1\right)}$$ is equal to

If $$f(x) = -x^2 - 3x^2 - 2x + a:a \in R$$, then the real values of $$x$$ satisfying $$f(x^2 + 1) > f(2x^2 + 2x + 3)$$ will be:-

If $$f\left(y\right)=\log y$$, then $$f\left(y\right)+f\left(1/y\right)$$ is equal to 

$$f(x)=\begin{cases} 5,\ \ \  \ \  \ \ x \le 1 \\ a+bx,\ \ 1 < x < 3 \\ b+ax , \ \ \ 3 \le x < 5 \end{cases}$$ then what is the value of $$a,b$$.

If $$fxln\left(1+\dfrac{1}{x}\right)dx=p(x)ln\left(1+\dfrac{1}{x}\right)+\dfrac{1}{2}x-\dfrac{1}{2}ln(1+x)+c$$, being arbitary costant, then

If $$\emptyset (x)=\emptyset '(x)$$  and $$\emptyset (1)=2,$$ then $$\emptyset (3)=?$$

If the function $$f:[2,\infty ]\rightarrow [1,\infty ]$$ is defined by $$f(x)=3^{x}(x-2)$$ then $$f^{-1}(x)$$  is