Question

Which quadrants and axes does `f(x)=cos(sqrtx)` pass through?

Answer 1

quadrants `I` and `IV` and both axes

(for `x in RR`)

Explanation:

If you work in `RR`:

`sqrtx in RR iff x>=0`
`=>` quadrants `II` and `III` are not relevant...

`f_((0))=cos(sqrt0)=cos0=1`
`(0,1)`
`f_((x))=0 => cos(sqrtx)=0 => sqrtx=pi/2 =>x=pi^2/4>0`
`(pi^2/4,0)`
`=>` both axes

`f_((pi/2))=cos(sqrt(pi/2))=+0.312175571143>0`
`f_(((5pi)/2))=cos(sqrt((5pi)/2))=-0.943055404868<0`
`=>` quadrants `I` and `IV`