Which quadrants and axes does $f (x) = cos (\sqrt{x})$ $f(x)=cos(sqrtx)$ pass through?

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Answer 1 · 2017-11-26T23:12:54

quadrants $I$ $I$ and $I V$ $IV$ and both axes

(for $x in RR$ )

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 $IV$

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