If a function $f: Z \rightarrow Z$ is defined by $f(x) = x - (-1)^x$,then $f(x)$ is

Let $f: X \rightarrow X$ be such that $f(f(x)) = x$ for all $x \in X$ and $X \subseteq \mathbb{R}$. Then:

$f : R \to R$ is defined as $f(x) = \begin{cases} x^2 + 2mx - 1, & x \leq 0 \\ mx - 1, & x > 0 \end{cases}$. If $f(x)$ is one-one,then the set of values of $m$ is:

Let $f: R \rightarrow R$ be a function defined by $f(x) = \frac{e^{|x|} - e^{-x}}{e^x + e^{-x}}$, then

Let $f(x) = \begin{cases} x \sin \left(\frac{1}{x}\right) & \text{when } x \neq 0 \\ 1 & \text{when } x = 0 \end{cases}$ and $A = \{x \in \mathbb{R} : f(x) = 1\}$. Then,$A$ has

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: