Question

The number of real solutions `cos(e^x)=2^x + 2^-x` is ?

Answer 1

See below.

Explanation:

`2^x+2^-x` is an even function with minimum at `x = 0`

or `2 le 2^x+2^-x`

also we know that

`-1 le cos(y) le 1`

and the conclusion is that

`cos(y)` and `2^x+ 2^-x` does not intercept so no real solution is possible for

`cos(e^x)=2^x + 2^-x`