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ス) For each Funci injective, surjectie, both, ar neither. Give short justi ficatiums for you la) A= R, B= R : fxl=x*. (b) A= IR, B= IR,, : strat u answers. %3D 20 20

ス) For each Funci injective, surjectie, both, ar neither. Give short justi ficatiums for you la) A= R, B= R : fxl=x*. (b) A= IR, B= IR,, : strat u answers. %3D 20 20

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2) For each function f:A→B below, detkımine he the it is injective, surjecire, both, er neitheu. Give sthert justificatioms for Jotu answeis. la) A= R, B= R,i ful=x². (b) A = IR, B= R. f(x) = x. 20 ギ)= e 20 ic) A- R, B= R: f(x)=lnx. %3D (d) A=R, B=R: fx)=X. (e) A= ZxZ, B = 0 : fx;y) = 2 X +1 %3D If) A=R5= integers mod 5, B= R =inlepes med 5 %3D %3D 3 f (xmud 5) = x'mod 5. %3D (8) A is the set g di ffeentiaSle functions From R to R. B=R:f191=g'l1) I that is , the feunction takes its deriva tive at 1). Ia) A={xeZ|x = 3 mod 43, B= {xeZ|x=Imod 43;f(x) = x to ノ
Transcribed Image Text:2) For each function f:A→B below, detkımine he the it is injective, surjecire, both, er neitheu. Give sthert justificatioms for Jotu answeis. la) A= R, B= R,i ful=x². (b) A = IR, B= R. f(x) = x. 20 ギ)= e 20 ic) A- R, B= R: f(x)=lnx. %3D (d) A=R, B=R: fx)=X. (e) A= ZxZ, B = 0 : fx;y) = 2 X +1 %3D If) A=R5= integers mod 5, B= R =inlepes med 5 %3D %3D 3 f (xmud 5) = x'mod 5. %3D (8) A is the set g di ffeentiaSle functions From R to R. B=R:f191=g'l1) I that is , the feunction takes its deriva tive at 1). Ia) A={xeZ|x = 3 mod 43, B= {xeZ|x=Imod 43;f(x) = x to ノ
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