M L Aggarwal Solutions for Chapter: Relations and Functions, Exercise 4: EXERCISE 2.4

Find the domain and the range of the function $f\left(x\right)=\frac{1}{\sqrt{4-x^2}}$. 

Find the domain and the range of the function $f\left(x\right)=|x-3|$. 

Find the domain and the range of the function $f\left(x\right)=3-|x-2|$. 

Find the domain and the range of the real function $f\left(x\right)=\frac{\left|x\right|-x}{2x}$. 

Find the domain and the range of the function $f$ defined by $f\left(x\right)=\frac{|x-4|}{x-4}$. 

If $f$ and $g$ are two real functions defined by $f\left(x\right)=2x+1 \mathrm{and} g\left(x\right)=4x-7$, then for what real value of $x$ such that $f\left(x\right)=g\left(x\right) ?$

If $f$ and $g$ are two real functions defined by $f\left(x\right)=2x+1 \mathrm{and} g\left(x\right)=4x-7$, then for what real value of $x$ such that $f\left(x\right)<g\left(x\right) ?$

Find the domain for which the functions $f\left(x\right)=3x^2-1 \mathrm{and} g\left(x\right)=3+x$ are equal.