Inverse Functions

Let $f\left(x\right)=\left[x-1\right]+{\left\{x\right\}}^{\left\{x\right\}}$, $x\in \left(1,3\right)$, then $f^{-1}\left(x\right)$ is

Here, $\left[·\right]$ is GIF and $\left\{·\right\}$ is the fractional part function.

Let $f:\left(2,4\right)\to \left(1,3\right)$ be a function defined by $f\left(x\right)=\frac{x}{2}+\left\{\frac{x}{2}\right\}$, (where, $\left\{·\right\}$ is the fractional part function), then $f^{-1}\left(x\right)$ is

If $y=\frac{x^2+2x+1}{x^2+2x+7}$, then inverse function $x$ is defined only when

Let $f:R\to R$ be defined by $f\left(x\right)=\left\{\begin{array}{l}x+5, \text{if} x\le 0\\ x^2+5, \text{if} x>0\end{array}\right.$. Let $f^{-1}$ denotes the inverse of the function $f$ then $f^{-1}$ is given by 

If $f\left(x\right)={\left(2x-3\mathrm{\pi }\right)}^5+\frac{4}{3}x+\cos x$ and $g$ is the inverse of $f\left(x\right)$, then $g^{\text{'}}\left(2\mathrm{\pi }\right)$ is equal to

The function $f\left(x\right)=\frac{ax+b}{cx+d}$, whers $a,b,c,d$ are not zero real number. If $f\left(19\right)=19, f\left(97\right)=97$ and $f\left(f\left(x\right)\right)=x \forall R \& x\ne -\frac{d}{c}$. The number that is not in the range of $f\left(x\right)$ is

If $f:[-1,0)\to (-\infty ,-1]$ and $f\left(x\right)=\frac{\left[x\right]}{\left|x\right|}$, where [.] represents greatest integer function. Then $f^{-1}\left(x\right)$ is equal to

Let a real valued function satisfies, $10\left[f\left(x\right)+\ln f\left(x\right)\right]=x^3$ for all positive $x$. Number of solutions of $f\left(x\right)=f^{-1}\left(x\right), x\in A$, where $A$ is the set of values of $x$ for which $f\left(x\right)$ is invertible, is

Let $A=R-\left\{3\right\}$ and $B=R-\left\{1\right\}$, then $f: A\to B$ is defined by $f\left(x\right)=\frac{x-2}{x-3}$. What is the value of $f^{-1}\left(\frac{1}{2}\right)$?

$f\left(x\right)=2x^3+1$ then what is $f^{-1}\left(x\right)$ options

Number of real numbers $x$ satisfying equation $x^3-8=16\sqrt[3]{x+1}$ are

If $f:R\to R, f\left(x\right)=x^3+3$, and $g:R\to R, g\left(x\right)=2x+1$, then $f^{-1}o{g}^{-1}\left(23\right)$ equals

The inverse function of the function $f\left(x\right)=9x^2+12x+16$ is

Let $a>1$ be a real number and $f\left(x\right)={\log }_a{x}^2$ for $x>0 .$ If $f^{-1}$ is the inverse function of $f$, and $b$ and $c$ are real numbers, then $f^{-1}\left(b+c\right)$ is equal to

Let $\mathrm{S}=\{a,b,c\}$ and $\mathrm{T}=\{1,2,3\}$. Find $f^{-1}$ of the following function $f=\left\{\right(a,2),(b,1),(c,1\left)\right\}$ $f$ from $S$ to $T$, if it exists.

If $f : R \to R, f\left(x\right)=\cos (x + 2)$  , does $f^{-1}$ exist?

State with reason whether the function $h:\{2,3,4,5\}\to \left\{7,9,11,13\right\}$ with $h=\left\{\left(2,7\right),\left(3,9\right),\left(4,11\right),\left(5,13\right)\right\}$  have inverse.

Let $f:X\to Y$ be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $(f^{-1}{)}^{-1}$ $=f.$

Write the properties of inverse function?