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

If $f(x) = \frac{x - |x|}{|x|}$,then $f(-1) = $

Let $f, g: R \rightarrow R$ be defined,respectively,by $f(x) = x + 1$ and $g(x) = 2x - 3$. Find $f+g$,$f-g$,and $\frac{f}{g}$.

Let the function $f:[0,1] \rightarrow \mathbb{R}$ be defined by $f(x) = \frac{4^x}{4^x+2}$. Then the value of $f\left(\frac{1}{40}\right) + f\left(\frac{2}{40}\right) + f\left(\frac{3}{40}\right) + \dots + f\left(\frac{39}{40}\right) - f\left(\frac{1}{2}\right)$ is:

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

Let $\alpha, \beta$ and $\gamma$ be three positive real numbers. Let $f(x) = \alpha x^5 + \beta x^3 + \gamma x, x \in \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be such that $g(f(x)) = x$ for all $x \in \mathbb{R}$. If $a_1, a_2, a_3, \dots, a_n$ are in arithmetic progression with mean zero,then the value of $f(g(\frac{1}{n} \sum_{i=1}^{n} f(a_i)))$ is equal to.