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f-x-x-3-e-x-3-e-f-1-

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Question Number 12403 by sin (x) last updated on 21/Apr/17
f(x)=⌊x−(3/e)⌋+⌊x+(3/e)⌋⇒f(1)=?
f(x)=⌊x−3e⌋+⌊x+3e⌋⇒f(1)=?
Answered by FilupS last updated on 21/Apr/17
⌊x⌋ = floor(x) f(1)=⌊1−(3/e)⌋+⌊1+(3/e)⌋ 2e>3>e ⇒ 2>(3/e)>1 ∴−1<1−(3/e)<0 ⇒ ⌊1−(3/e)⌋=−1 ∴2<1+(3/e)<3 ⇒ ⌊1+(3/e)⌋=2 ∴f(1)=−1+2 f(1)=1
⌊x⌋=floor(x)f(1)=⌊1−3e⌋+⌊1+3e⌋2e>3>e⇒2>3e>1∴−1<1−3e<0⇒⌊1−3e⌋=−1∴2<1+3e<3⇒⌊1+3e⌋=2∴f(1)=−1+2f(1)=1

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