Is the following ufnction invertible?

Question

If so, find its inverse
T(t) = t^2 - 6t + 12

Answer 1

THEOREM: A function is invertible if and only if it is one-to-one and onto.

This statement is a theorem that requires proof! You should investigate this and learn how to prove this theorem. In any event, here is how you use it:

CLAIM: T(t) is not invertible.

PROOF: T(t) is not one-to-one since T(2) = T(4) = 4. T(t) is not onto since D = (-inf, inf) and R = [3, inf). Since T(t) is neither one-to-one nor onto, it follows that the function is not invertible. QED

Answer 2

No, a quadratic polynomial is not invertible to a function as the inverse would have two values except at the vertex.

Answer 3

No it is not invertible. No polynomial of even degree is invertible because they are not one to one.