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Question Number 184893 by mnjuly1970 last updated on 13/Jan/23
find the set of critical points for: 1: f (x) = (x/(⌊ x ⌋+⌊ −x⌋)) −x 2 : g(x) = (x/(⌊ x ⌋ +⌊ −x ⌋)) +x
findthesetofcriticalpointsfor:1:f(x)=x⌊x⌋+⌊−x⌋−x2:g(x)=x⌊x⌋+⌊−x⌋+x
Answered by Mathspace last updated on 13/Jan/23
1) x in Z ⇒[x]+[−x]=0⇒f is not defined x ∉Z ⇒[x]+[−x]=−1 ⇒ f(x)=(x/(−1))−x=−2x any way we have D_f =R−Z 2)g(x)not defined for x ∈Z and for x∉Z g(x)=(x/(−1))+x=0 ⇒D_g =R−Z
1)xinZ⇒[x]+[−x]=0⇒fisnotdefinedx∉Z⇒[x]+[−x]=−1⇒f(x)=x−1−x=−2xanywaywehaveDf=R−Z2)g(x)notdefinedforx∈Zandforx∉Zg(x)=x−1+x=0⇒Dg=R−Z
Commented by mnjuly1970 last updated on 19/Jan/23
thx alot
thxalot

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