R D Sharma Solutions for Chapter: Functions, Exercise 2: EXERCISE 3.2

If $f\left(x\right)=\left\{\begin{array}{l}{x}^2,\text{ when }x<0\\ x,\text{ when }0\le x<1\\ \frac{1}{x},\text{ when }x>1\end{array}\right.$, then find $f\left(-2\right)$.

If $f\left(x\right)=\left\{\begin{array}{l}{x}^2,\text{ when }x<0\\ x,\text{ when }0\le x<1\\ \frac{1}{x},\text{ when }x>1\end{array}\right.$, then find $f\left(\sqrt{-3}\right)$.

If $f\left(x\right)=\left\{\begin{array}{l}{x}^2,\text{ when }x<0\\ x,\text{ when }0\le x<1\\ \frac{1}{x},\text{ when }x>1\end{array}\right.$, then find $f\left(\sqrt{3}\right)$.

If $f\left(x\right)=\left\{\begin{array}{l}{x}^2,\text{ when }x<0\\ x,\text{ when }0\le x<1\\ \frac{1}{x},\text{ when }x>1\end{array}\right.$, then find $f\left(1\right)$.

If $f\left(x\right)=\frac{x-1}{x+1}$, then show that $f\left(-\frac{1}{x}\right)=-\frac{1}{f\left(x\right)}$.

If for non-zero $x$, $af\left(x\right)+bf\left(\frac{1}{x}\right)=\frac{1}{x}-5$, where $a\ne b$, then find $f\left(x\right)$.

Find the domain of the following real valued function of real variable:

$f\left(x\right)=\frac{1}{x-7}$

Find the domain of the following real valued function of real variable:

$f\left(x\right)=\frac{3x-2}{x+1}$