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

1 Answer
Nov 26, 2017

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