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# 20190329_003730.jpg - 12 4)` Defire F 2 D Z by the rule FLA...

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Unformatted text preview: 12 ) 4 )` Defire_ F : 2 _ D Z by the rule_ FLA ) = 2 - 3 ~ , for all\ integers ~` i) is F one to one ? Prove or give a counter example_ ii) isf onto ? Prove of give a counter example_ b ) Define G : R _ R. by the relle G( X ) : 2 - 3 x for all real numbers x. Is G onto? Pace or give a counter excomple a ) ;) of is one to one : Suppose f (` ) = FLAz ) for some integers My and rec By definition of F : 2 - 30, = 2- 3 ~` \= - 3 21 = = 3 ~` = ME = N Z So f is one to one_ ii ) f is not onto : Consider 3 E Z we claim that } { FLA)? for any integer ~ , because if there were an integer ~ such that 3 = f(m ), Then by chefinition off, 3= 2 - 3~` = 1 = - 3 ~ - - 3 : ~ - I is not an integer , Hence 3 7 flow) for any integer ~` and so F is not on to 6 ) G is onto : Suppose y ER. since YER, `y = 2 - 3 x = 4 - 2 - 3 X X - = 7- 2 = 2-7 = x Itlace there exists an integer Such They g(x ) = Y . As was to be shown...
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• Fall '19
• NoProfessor
• Philosophy of language, Rational number, Define G

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