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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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