# one to one function with unknown constant!

• December 6th 2007, 09:06 AM
runner07
one to one function with unknown constant!
This problem is driving me crazy.

Let f(x)= 3x^3 + kx^2 +5x, k is a constant. For what values of k is f one to one?

I tried using b^2 -4ac from the Quadratic Formula but I didn't get the same answer as the answer choices...
a. |k| <= 3 root5
b. 5/9 <= k
c. |k|<= 6 root5
d. k <= 5/9
e. 3 root5 <= |k|

• December 6th 2007, 09:19 AM
colby2152
A function f(x) is one-to-one if and only if f(x) has an inverse. Another way to determine if a function f(x) is one-to-one is to test values, therefore if for every a and b in its domain, f(a) = f(b) implies a = b.
• December 6th 2007, 09:26 AM
Plato
Quote:

Originally Posted by runner07
Let f(x)= 3x^3 + kx^2 +5x, k is a constant. For what values of k is f one to one?

Consider the derivative $f'(x) = 9x^2 + 2kx + 5$.
What are the values for k making that derivative nonnegative?
Why does that work?