If $f(x) = 2\sin x$ and $g(x) = \cos^2 x$,then $(f + g)\left(\frac{\pi}{3}\right) = $

The function $f(x) = [|x|] - |[x]|$ where $[x]$ denotes the greatest integer function:

Let $f'(x) > 0$ and $g'(x) < 0$ for all $x \in R$. Then which of the following is true?

If $e^{f(x)}=\frac{10+x}{10-x}, x \in(-10,10)$ and $f(x)=k f\left(\frac{200 x}{100+x^2}\right)$,then $k$ is equal to

If $f(x)$ is a real-valued function defined by $f(x) = \frac{a x^{10} + b x^8 + c x^6 + d x^4 + e x^2 + 12 x + 15}{x}$ for $x \neq 0$ and $f(4) = -4$,then find the value of $f(-4)$.

If $f(x) = 4x^3 + 3x^2 + 3x + 4$,then $x^3 f\left( \frac{1}{x} \right)$ is