Question

Prove that 2x+cosx has exactly 1 root

(preferably using proof by contradiction)

Answer 1

probably take the derivative and show that the function is always increasing
that would be my guess

Answer 2

If I derive the function, I get y= 2+sinx.

I try to find the critical values, but I get sinx=2.
The sin function is bounded by 1 and -1, so cannot be 2