Question

$$\begin{array}{cc}coloumn1& coloumn2\\ a& p)\frac{1}{x}\\ b& q)\frac{1}{x^2}\\ c& r)\frac{1}{x^3}\\ d& s)\frac{1}{x^4}\end{array}$$

• A. a - s; b - q; c - p; d - r
• B. a - s; b - p; c - r; d - q
• C. a - s; b - p; c - q; d - r
• D. a - p; b - q; c - r; d - s

Answer 1

The correct option is A

a - s; b - q; c - p; d - r

We saw that graphs of $x^2,x^4,x^6..........$ looks similar. Similarly, the graphs of $\frac{1}{x^2},\frac{1}{x^4},\frac{1}{x^6}.........$

They all look like

So, the graphs in figure two are of $\frac{1}{x^2}$ and $\frac{1}{x^4}$ . We want to distinguish them now. If x $>$ 1 ,$x^2$ $<$ $x^4$ $\Rightarrow$ $\frac{1}{x^2}$ $>$ $\frac{1}{x^4}$ .

So we look in the interval x $>$ 1 and say the graph which lies above is that of $\frac{1}{x^2}$.

The next figure will be of $\frac{1}{x^3}and\frac{1}{x}$ . They both look like

We will follow the same logic to distinguish between them. If $x>1$ ,$x^3$ $>$ x $\Rightarrow$ $\frac{1}{x}$ $>$ $\frac{1}{x^3}$

The graph which lies above will be the graph of $\frac{1}{x}$ if x $>$ 1