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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- CSIR NET
- Mathematical Sciences
In r) br op degrtehnest ni t:fa r) h (r) 1s map rintd b fa)_ xjuy_ then set o al olynomials over r wh'th omy bi neu hon (o rree t 1s lintav or not ll onto nej t
In R) br Op degrtehnest ni T:fa R) h (R) 1s Map rintd b Fa)_ XJUY_ then set o al olynomials over R wh'th omy bi neu hon (o rree T 1s Lintav or not lL onto nej twr bofh
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Navdeep goyal 1 Best Answer
T((af+bg)(x))=x(af+bg)'(x) =x{ af'(x)+bg'(x)} =a{xf'(x)}+b{xg'(x)} =aT(f)+bT(g) T is linear T is not one one onto bcz T(2)=0 T(3)=0 But 2≠3 T is not one one Pre image of constant does not exist so not onto