Question

How do you graph `f(x)=2cosx-(sqrt2)` and solve over the interval [0,2pi)?

Answer 1

The graph of `f(x) = 2 cos(x) - ( sqrt(2) )`
is simply the graph of `2 cos(x)` shifted down by `( sqrt(2) )`
(where `2 cos(x)` is simply `cos(x)` stretched vertically by a factor of `2`).

I was not certain what you meant by "solve"; I have assumed you meant:
solve for `x` when `2 cos(x) - ( sqrt(2) ) = 0`

`2 cos(x) - sqrt(2) = 0`

`2 cos(x) = sqrt(2)`

`cos(x) = ( 1 / sqrt(2) )`

(This is a standard #45^o angle)

Within the specified range `f(x) = 0`
when
`x = 45^o` (`Pi/4` radians)
and
`x = 315^o` (`(7Pi)/4` radians)