find analytically the x coordinate where the two function intersect each other
F(x) = e^2x/ e^x + 1 and G(x) = 2/3 - e^ x
Answers
Answer :
The point of intersection of these functions , f(x) = e^2x/e^x + 1 and g(x) = ⅔ - e^x are :
1. ( -0.693 , 0.167 )
2. ( -0.405 , 0 )
3. ( 0, -0.333 )
Here , the x coordinate where they intersect can have three values , x_int = -0.693 , = -0.405 and 0
Explaination :
First see the graph of e^x .
This is an increasing monotonic function , with the domain ranging from (-∞ to ∞ ) .
The graph will be opposite to that of a logarithmic function .
The domain, similar to that of other exponential functions is all real numbers .
So , using this , we can convert in the following steps :
f(x) = e^x
- f(x) = -e^x
To get 2/3 - e^x , shift this graph by a magnitude of 2/3 towards the left .
Similarly for the first one we need to simplify in a similar way to get the required graph .
Now you can easily find the intersection points .
It's recommended to use a graph plotting software while experimenting with this for accuracy .
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