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Question Number 184942 by mnjuly1970 last updated on 14/Jan/23
f(x )= x + ⌊ x + (( ⌊ x_ ^ ⌋)/(⌊ (x^( 2) /(1 +x^( 2) )) ⌋+1)) ⌋ ⇒ f^( −1) (x )=?
f(x)=x+⌊x+⌊x⌋⌊x21+x2⌋+1⌋⇒f−1(x)=?
Commented by Frix last updated on 14/Jan/23
f(x)=x+2⌊x⌋ −2≤x<−1: f(x)=x−4∧−6≤f(x)<−5 −1≤x<0: f(x)=x−2∧−3≤f(x)<−2 0≤x<1: f(x)=x∧0≤f(x)<1 1≤x<2: f(x)=x+2∧3≤f(x)<4 2≤x<3: f(x)=x+4∧6≤f(x)<7 n≤x<n+1: f(x)=x+2n∧3n≤f(x)<3n+1∀n∈Z ⇒ f^(−1) (x) is not defined for 3n−2≤x<3n∀n∈Z f^(−1) (x)=x−2n; 3n≤x<3n+1∀n∈Z
f(x)=x+2⌊x⌋−2⩽x<−1:f(x)=x−4∧−6⩽f(x)<−5−1⩽x<0:f(x)=x−2∧−3⩽f(x)<−20⩽x<1:f(x)=x∧0⩽f(x)<11⩽x<2:f(x)=x+2∧3⩽f(x)<42⩽x<3:f(x)=x+4∧6⩽f(x)<7n⩽x<n+1:f(x)=x+2n∧3n⩽f(x)<3n+1∀n∈Z⇒f−1(x)isnotdefinedfor3n−2⩽x<3n∀n∈Zf−1(x)=x−2n;3n⩽x<3n+1∀n∈Z
Commented by mnjuly1970 last updated on 14/Jan/23
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