If it is not an onto function, provide the range.(adsbygoogle = window.adsbygoogle || []).push({});

I have problems with these two

g: R -> R

g(x) = x^2 + x

g(x) = x^3

The book said g1 is neither onto nor 1-1, while g2 is both

I see how x^2 + x is not `1-1 function. But how come it is not onto? I mean R is real number, can be 343.3434534564656757 or 67.23123132 or anything that is real number. How can we quickly show that x^2 + x is not onto? There are -inf, inf real numbers, so how can we say there is a particular g(x) left out?

One way I see is if x^2 + x = 0 and we get x = sqrt(-x) which is an i num

I see x^3 is a 1-1 because x1 = x2. in a similar way as in the case of g1, how can we be so sure that all real numbers can be produce?

In the book, things like x^3 its surjectiveness can be proven as following

x^3 and if r is any real number in codomain of f, then real number cubic root of r is in the domain of f and since f(cubic root of r) = (cubic root of r)^3 = r, so f = R = range of f, so it is onto (copied from book)

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Determine whether it is an onto function

**Physics Forums | Science Articles, Homework Help, Discussion**