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## Homework Statement

Find a function where the domain is integers, codomain is real numbers, and image isn't equal to codomain.

## Homework Equations

## The Attempt at a Solution

I know that it means that when I plug in an integer I will obtain a real number, but how do I make it so that the image is not equal to the codomain? I don't quite understand what that means. Does it mean the function is injective?

Here is what I have so far for my first attempt:

f: ℤ→ℝ

f(x)=√x

^{4}+5

However if my x is 2 and -2 I get the same answer. So I am struggling with how to get an injective function.

However here is my second attempt:

f: ℤ→ℝ

f(x) = 1/(x

^{3}-3)

Is my second attempt correct?

Thank you.