Functions

Let $A=\left[-1,1\right]$ and $f:A\rightarrow\,A$ be defined as $f\left(x\right)=x\left|x\right|$ for all $x\in\,A$, then $f\left(x\right)$ is

Number of real solution of $\sqrt{5-\log _2|x|}$ $=3-\log _2|x|$ is equal to

Let $[x]$ denote the greatest integer $\leq x$. If $f(x)=[x]$ and $g(x)=|x|$, then the value of $f\left(g\left(\frac{8}{5}\right)\right)-g\left(f\left(-\frac{8}{5}\right)\right)$ is

If $f: R \rightarrow R, g: R \rightarrow \mathrm{R}$ are defined by $f(x)=5 x-$ $3, g(x)=x^2+3$, then $g o f^{-1}(3)$ is equal to

Let the function $g:(-\infty, \infty) \rightarrow\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ be given by $g(u)=2 \tan ^{-1}\left(e^u\right)-\frac{\pi}{2}$. Then, g is

If a function $\mathbf{f}: \mathbf{R}-\{l\} \rightarrow \mathbf{R}-\{m\}$ defined by $f(x)=\frac{x+3}{x-2}$ is a bijection, then $3 l+2 m=$

Consider the function $\mathrm{f}$ in $\mathrm{A}=\mathrm{R}-\left\{\frac{2}{3}\right\}$ defined as $f(x)=\frac{4 x+3}{6 x-4}$, then $f^{-1}$ is equal to

The domain of the function $f(x)=\sqrt{x-\sqrt{1-x^2}}$ is

If $f(x)=\frac{x}{\sqrt{1+x^2}}$, then (fof of) $(x)$ is

If $g(x)=x^2+x-2$ and $\frac{1}{2} g o f(x)=2 x^2-5 x+2$ then $f(x)$ is equal to

The domain of the function $\mathrm{f}(x)=\frac{1}{\sqrt{x^{12}-x^{9}+x^{4}-x+1}}$ is given by

The domain of the function $f(x)=\sqrt{x-\sqrt{1-x^{2}}}$ is