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Last updated at May 29, 2018 by Teachoo
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Misc 5 Show that the function f: R R given by f(x) = x3 is injective. f(x) = x3 We need to check injective (one-one) f (x1) = (x1)3 f (x2) = (x2)3 Putting f (x1) = f (x2) (x1)3 = (x2)3 x1 = x2 Since if f (x1) = f (x2) , then x1 = x2 It is one-one (injective)
To prove one-one & onto (injective, surjective, bijective)
Onto function
One One and Onto functions (Bijective functions)
Example 7
Example 8
Example 9
Example 11 Important
Misc 5 You are here
Ex 1.2, 5 Important
Ex 1.2 , 6
Example 10
Ex 1.2, 1
Ex 1.2, 12
Ex 1.2 , 2 Important
Ex 1.2 , 7
Ex 1.2 , 11
Example 12 Important
Ex 1.2 , 9
Ex 1.2 , 3
Ex 1.2 , 4
Example 50
Example 51 Important
Ex 1.2 , 10 Important
Misc. 4 Important
Example 13 Important
Example 14 Important
Ex 1.2 , 8 Important
Example 46 Important
Misc 10 Important
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