Dear all,
please help me solving this question
Determine whether the function is injective or surjective.
f (X) = X3 – X
Do you know what the terms mean?
Injective = For any a and b in the domain, f(a) = f(b) implies a = b. (They map to distinct elements)
Surjective = For any y in the range, there exists an x such that f(x) = y. (Every element in the range has a corresponding element in the domain)
Assuming you mean $\displaystyle f(x) = x^3 - x $ then you can factor it and see if the two properties hold.
Hint: Look at the roots of the polynomial. Also, is this in the reals or the complex?
Asked (by a different member it would seem) and answered here: http://www.mathhelpforum.com/math-he...nly-maths.html