Finding the x-intercept of f(x) = x + cos(x)

[swjafar]

f(x) = x + cos(x)
I found the y-intercept to be 1
f(0) = 0 + cos(0) = 1

However, when trying to solve for f(x) = 0, I get -x = cos(x).

From this point it seems to be a trial and error game or calls for the use of some complex function to solve for x. Is there a simpler way?

 

[tkhunny]

f(x) = x + cos(x)
I found the y-intercept to be 1
f(0) = 0 + cos(0) = 1

However, when trying to solve for f(x) = 0, I get -x = cos(x).

From this point it seems to be a trial and error game or calls for the use of some complex function to solve for x. Is there a simpler way?

No, I think you have it. There are many interesting methods for finding numerical solutions where your algebraic efforts prove insufficient. Some require the Calculus. (derivatives can be helpful.) Some don't.