Embibe Experts Solutions for Exercise 7: Assignment

Let $f\left(x\right)=\frac{1}{2}+\sqrt{x-\frac{3}{4}}$ and $\varphi \left(x\right)=f^{-1}\left(x\right)$ then $\varphi \left(3\right)$ equals..

Let $f:R\to R$ and $g:R\to R$ be two given functions defined as $f\left(x\right)=3x^2+2$ and $g\left(x\right)=3x-1,\forall x\in R$ Then $\frac{1}{2}\sqrt{\left[\right(gof\left)\right(x\left)\right]\left[fog\right(x\left)\right]}$ at $x=1$ is......

Let $S=\{1,2,3,4\}$. The number of functions $f:S\to S$. Such that $f\left(\mathrm{i}\right)\le 2i$ for all $i\in S$ is equal to $2^k$ where $k$ is equal to..........

Let $A=\{1,2,3,4\}$. The number of functions $f:A\to A$ satisfying $f\left(f\right(i\left)\right)=i$ for all $1\le i\le 4$ is -

Let $f:\{1,2,3\}\to \{1,2,3\}$ be a function. If the number of functions $g:\{1,2,3\}\to \{1,2,3\}$. Such that $f\left(x\right)=g\left(x\right)$ for atleast one $x\in \{1,2,3\}$ is $k$, then $(k-10)$ is equal to

Let $f:(-2,2)\to (-2,2)$ be a continuous function such that $f\left(x\right)=f\left(x^2\right)\forall x\in d_f$ and $f\left(0\right)=\frac{1}{2}$, then the value of $4f\left(\frac{1}{4}\right)$ is equal to

Let $A=\left\{x_1, x_2, x_3, x_4, x_5\right\}, B=\left\{y_1, y_2, y_3, y_4\right\}.$ A function $\text{'}f\text{'}$ is defined from $A$ to $B$, such that $f\left(x_1\right)=y_1$ and $f\left(x_2\right)=y_2$, if the number of onto functions from $A$ to $B$ is $n$, then $(n-10)$ is

The area enclosed by the curve $|x+y-1|+|2 x+y+1|=1$ in square units is