Could someone help me with one-to-one functions?

So one of the exercises in the homework is :

g(x) = x^3+kx is one-to-one for k>0

f(x) = x^3+3x^2+kx

For what value of k is f(x) one to one?

I know that a function is 1-1 if x=y and f(x)=f(y) but then I don't know how I can figure out the value of k. Could someone please explain to me how I can do this so I can do it myself next time?

PS: There was a hint in the exercise which is: "write f(x) in the form (x - a)^3, and

determine the value for a for which f(x) reduces to the form of g(x); the squared term vanishes. Use then

the result for g(x)"

Thanks beforehand!