Embibe Experts Solutions for Chapter: Functions, Exercise 1: AMU-AT (B.Tech.) 2017

It $a, b$ be two fixed positive integers such that $f\left(a+x\right)=b+{\left[b^3+1-3b^{2}f\left(x\right)+3b{\left\{f\left(x\right)\right\}}^2-{\left\{f\left(x\right)\right\}}^3\right]}^{1/3}$ for all real $x$ then $f\left(x\right)$ is a periodic function with period

The domain of the function $f\left(x\right)={\log }_{3+x}\left(x^2-1\right)$ is

If $f\left(x\right)={\sin }^{2}x$ and the composite function $g\left(f\left(x\right)\right)=\left|\sin x\right|$, then the function $g\left(x\right)$ is equal to

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

The equation $\left|x\right|+\left|\frac{x}{x-1}\right|=\frac{x^2}{|x-1|}$ will be always true for $x$, belonging to

If $R$ is the set of real numbers and $f:R\to R$ is a function defined by $f\left(x\right)=\sin x,$ then $f^{-1}\left(\right[-1,1\left]\right)$ is

The range of the function $f\left(x\right)=\frac{2+x}{2-x}, x\ne 2$ is