Practice question · True or false
Every function from the integers to the integers is surjective.
Hints
- Surjective means every element of the codomain is actually produced.
- Consider a function whose outputs are always even.
Show the answer
False
Why
False. f(n) = 2n has codomain the integers but its image is only the even integers, so odd numbers are never reached. Declaring a codomain does not oblige the function to fill it.
Practise Functions as Mappings
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More questions on Functions as Mappings
- Let f have domain {-2, -1, 0, 1, 2} and rule f(n) = n squared. How many distinct elements are in its image?
- Let f(n) = 2n with domain and codomain the integers. Select every integer that IS in the image of f.
- The rule "send x to its square root" is not a function on the reals, but √x is. What was fixed?
- A function must assign exactly one output to each input. Why does the "exactly one" requirement do more work…
- Order the steps of a proof that f(n) = 3n - 2 is injective.
- A function assigns exactly one output to each input. Sort each correspondence.
- Complete the definition of an injective function.