If $f: R \rightarrow R$ is defined by $f(x)=2x+\sin x, x \in R$,then $f$ is

For functions $f$ and $g$,where $f: [0, \frac{\pi}{2}] \rightarrow R$ with $f(x) = \sin x$ and $g: [0, \frac{\pi}{2}] \rightarrow R$ with $g(x) = \cos x$,which of the following is true?

If $f(x) = (\frac{3}{5})^x + (\frac{4}{5})^x - 1$,$x \in R$,then the equation $f(x) = 0$ has

The function $f: N-\{1\} \rightarrow N$ defined by $f(n) = \text{the highest prime factor of } n$ is:

Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be the functions defined by $f(x) = \frac{x}{1+x^2}$ and $g(x) = \frac{x^2}{1+x^2}$. Then,the correct statement$(s)$ among the following is/are:

For the mapping $f: R-\{1\} \rightarrow R-\{2\}$,given by $f(x)=\frac{2x}{x-1}$,which of the following is correct?