If A=(x,y):y=e2x,x∈R and B=(x,y):y=e−2x,x∈R then nA∩B=

# If $\mathrm{A}=\left\{\left(\mathrm{x},\mathrm{y}\right):\mathrm{y}={\mathrm{e}}^{2\mathrm{x}},\mathrm{x}\in \mathrm{R}\right\}$ and $\mathrm{B}=\left\{\left(\mathrm{x},\mathrm{y}\right):\mathrm{y}={\mathrm{e}}^{-2\mathrm{x}},\mathrm{x}\in \mathrm{R}\right\}$ then $n\left(\mathrm{A}\cap \mathrm{B}\right)=$

1. A
2. B
3. C
4. D

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### Solution:

Given,$\mathrm{A}=\left\{\left(\mathrm{x},\mathrm{y}\right):\mathrm{y}={\mathrm{e}}^{2\mathrm{x}},\mathrm{x}\in \mathrm{R}\right\}$

$⇒$A is the set of all points on the graph of y = e2x

and $\mathrm{B}=\left\{\left(\mathrm{x},\mathrm{y}\right):\mathrm{y}={\mathrm{e}}^{-2\mathrm{x}},\mathrm{x}\in \mathrm{R}\right\}$

$⇒$B is the set of all points on the graph of $y={e}^{-2x}$

Now, we plot the graph of given sets

since , the graph of  intersect at one point.

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