# Thread: Surjectivity of (x^3) +5

1. ## Surjectivity of (x^3) +5

How can I prove the surjectivity of this function? I know I'm trying to prove that for all y in the range there exists an x in the domain such that $y=x^3$, but I can't think how to go about proving it. Thanks.

2. Originally Posted by Greengoblin
How can I prove the surjectivity of this function?
Does $\sqrt[3]{{y - 5}}$ exist fo every y?

3. Ah yes thanks. I was trying to show it's onto in order to show that it has an inverse, but I didn't think to try it the other way round.