Find the number of solutions of ` |x|*3^(|x|) = 1`.

Answer

2

Explanation

We have ` |x|3^(|x|)=1`
` or |x| = 3^(-|x|)`
Now, ` 3^(-|x|) ={{:(3^(-x)",",x ge 0),(3^(x)" ,",x lt 0):}`
To find the number of roots of the above equation, we need to find the number of points of intersection of `y=|x| and y = 3^(|x|)`
The graphs of these functions are as shown in the following figure:
` (##CEN_TRI_C01_E01_006_S01.png" width="80%">
From the fraph number of solution is 2.