"on to" functions?

Question

I was wondering if
f(x) = 1-x^3 (f:D ->R)
is an "on to" function. I did get to x= 1-y (with a root to the 3rd)
but i couldn't decide if the function is "on to"

thanks for the help

Answer 1

The question you need to ask yourself is " for every y in R, does my equation for x give me a value of x in the domain D?" If so, then every y is "hit" by f and the function is onto.

Answer 2

The range is R (all real numbers). Are there any real numbers that are not hit? any real numbers that are hit more than once.

If no to both, then onto.
If yes to either, then not onto.

Pick a number in the image (or 'y' as you put it). Is it always possible to find a number for x, such that 1-x^3 = y ? Is there always only one such number in x?

If yes to both: onto.