1. ## injective function

Dear all,

Determine whether the function is injective or surjective.

f (X) = X3 – X

2. 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 $f(x) = x^3 - x$ 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?

3. Originally Posted by zeeshan4u3
Dear all,