what is the f(x) of 2cosx=e^x, how can we solve its root?

Question

in this problem, how can i change this equation to this form, f(x)=function of x), in other words, what will be y?

Answer 1

In order to 'solve' for an equation, bring all the variables to one side and solve for zero. In this case,
y=2cosx - e^x OR
y=e^x - 2cosx
Then, to solve its root, make y=0 and solve for x. As far as I can see, the easiest way to do this is a graphics calulator. Put in the function and find the x-intercept. The x co-ordinate is your root.

Answer 2

This is a transcendental relationship and there is no closed form solution. Only numerical solutions are possible. You can use Excel to numerically solve this.

Since e^x is monotonically positive, while cos(x) goes to 0 at pi/2, the positive solution must be between 0 and pi/2