Embibe Experts Solutions for Chapter: Functions, Exercise 1: Level 1

If $f:R\to S$ is defined by $f\left(x\right)=4\sin x-3\cos x+1$ is an onto function, then what $S$ is equal to ?

Let $f:(1,\infty )\to [1,\infty )$ be defined by $f\left(x\right)=\frac{x+2}{x-1}.$ Then,

Let $\left[x\right]$ denote the greatest integer less than or equal to $x.$ Then, the values of $x\in R$ satisfying the equation ${\left[e^x\right]}^2+\left[e^x+1\right]-3=0$ lie in the interval:

Define $f: R\to R$ by $f\left(x\right)=\max \{x+1, 1-x, 2\}.$ Then $f$ is $\_\_\_$

If $f\left(x\right)=\frac{4x+x^4}{1+4x^3}$and $g\left(x\right)=\ln \left(\frac{1+x}{1-x}\right)$ then what is the value of $fog\left(\frac{e-1}{e+1}\right)$ $?$

Let $f:R\to R$ be defined as $f\left(x\right)=2 x-1$ and $g:R-\left\{1\right\}\to R$. be defined as $g\left(x\right)=\frac{x-\frac{1}{2}}{x-1}$. Then the composition function $f\left(g\left(x\right)\right)$ is:

If $f$ is a function defined on $(0,1)$ by $f\left(x\right)=\max \{x-[x],-x-[x\left]\right\}$, then $\left(fofofof\right)\left(x\right)$ is equal to ([.] greatest integer function)

Let $f:R-\left\{3\right\}\to R-\left\{1\right\}$ be defined by $f\left(x\right)=\frac{x-2}{x-3}$. Let $g : R\to R$ be given as $g\left(x\right)=2x-3$. Then, the sum of all the values of $x$ for which $f^{-1}\left(x\right)+g^{-1}\left(x\right)=\frac{13}{2}$ is equal to