How to plot ?

Hello,

My function f(x) satisfies : x*exp(- f(x)) + exp(-2*f(x)) = 3*(x+1). How to plot the function f(x) ?

Thanks

Answer 1

[Walter Roberson]

If you have the symbolic toolbox, then you can construct an equality but replace f(x) with a variable such as fx. Solve for fx. My tests show there as being two solutions. The lower bound is 2*sqrt(6)-6

[Abdoulaye Thiam]

Thanks !

This is what you are saying. How do you found the lower bound 2*sqrt(6)-6 ?

 syms x   fz 
>> solve( x*exp(-fz)+exp(-2*fz)-3*(x+1),fz)
ans =
 log((x - (x^2 + 12*x + 12)^(1/2))/(6*(x + 1)))
 log((x + (x^2 + 12*x + 12)^(1/2))/(6*(x + 1)))

[Walter Roberson]

You have a square root. If the value inside the square root is negative then you get a complex result. So you have a boundary when the square root is 0, which occurs at the location I indicated.

[Abdoulaye Thiam]

Thanks