Question and Answers Forum

All Questions      Topic List

Relation and Functions Questions

Previous in All Question      Next in All Question      

Previous in Relation and Functions      Next in Relation and Functions      

Question Number 40090 by maxmathsup by imad last updated on 15/Jul/18

let f(x)= 1−[x]−[1−x] 1) prove that f is periodic with period 1 2) give a expression of f(x) when x∈[0,1[

letf(x)=1−[x]−[1−x]1)provethatfisperiodicwithperiod12)giveaexpressionoff(x)whenx∈[0,1[

Commented by math khazana by abdo last updated on 29/Jul/18

1) first we have f(x)=1−[x]−1−[−x] =−[x]−[−x] ⇒ f(x+1) =−[x+1]−[−(x+1)] =−[x]−1−[−x]+1=f(x) so f is periodic with T=1 2) if 0≤x<1 [x]=0 and −1<−x≤0 ⇒[−x]=−1 ⇒ f(x)=−[−x]=−(−1)=1 .

1)firstwehavef(x)=1−[x]−1−[−x]=−[x]−[−x]⇒f(x+1)=−[x+1]−[−(x+1)]=−[x]−1−[−x]+1=f(x)sofisperiodicwithT=12)if0⩽x<1[x]=0and−1<−x⩽0⇒[−x]=−1⇒f(x)=−[−x]=−(−1)=1.

Terms of Service

Privacy Policy

Contact: info@tinkutara.com