R S Aggarwal Solutions for Exercise 6: EXERCISE 3F

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

Let $f=\left\{\left(1,6\right),\left(2,5\right),\left(4,3\right),\left(5,2\right),\left(8,-1\right),\left(10,-3\right)\right\}$ and $g=\left\{\left(2,0\right),\left(3,2\right),\left(5,6\right),\left(7,10\right),\left(8,12\right),\left(10,16\right)\right\}$

Find : dom $\left(f+g\right)$.

Let $f=\left\{\left(1,6\right),\left(2,5\right),\left(4,3\right),\left(5,2\right),\left(8,-1\right),\left(10,-3\right)\right\}$

and $g=\left\{\left(2,0\right),\left(3,2\right),\left(5,6\right),\left(7,10\right),\left(8,12\right),\left(10,16\right)\right\}$

Find : dom $\left(\frac{f}{g}\right)$

If $f\left(x\right)=\frac{x-1}{x}$, find the value of $f\left\{f\left(\frac{1}{x}\right)\right\}$.

If $f\left(x\right)=\frac{\alpha x}{x+1}$, where $x\ne -1$ and $f\left\{f\left(x\right)\right\}=x$ for $x\ne -1$ then find the value of $\alpha$.

Find the range of the function, $f\left(x\right)=\frac{x}{\left|x\right|}$

Find the domain of the function, $f\left(x\right)=\log \left|x\right|$.

If $f\left(x+\frac{1}{x}\right)=\left(x^2+\frac{1}{x^2}\right)$ for all $x\in R-\left\{0\right\}$ then write an expression for $f\left(x\right)$.