Consider the function f: Z -> Z, where f(x) 4x+1 for each x is an element in Z, here the range of F = { ... -8, -5, -2, 1, 4, 7...} is a proper subset of Z, so f is not an onto (surjective) function.(adsbygoogle = window.adsbygoogle || []).push({});

When one examines 3x + 1 = 8, we know x = 7/3, so there is no x in the domain Z with f(x) = 8

But if g: Q -> Q, where g(x) = 3x+1 for x is an element in Q; and h: R -> R, where h(x) = 3x+1 for x is an element in R, both g and h are surjective function.

What I want to ask whether my understanding true or false:

1. We consider g is a valid surjective function because with x = 7/3, g(x) = 8, we can write 8/1, and so we consider it as a rational number

and

2. We consider h is surjective because 7/3 is a real number (we can alswo rewrite 7/3 as demcial...)

Thank you

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# Surjective function

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