Derivation question

1. Dec 28, 2008

1. The problem statement, all variables and given/known data

To derive the Bernsteine inequality

$$P[\left|f(x)\right| \ge z] \le 2e^{-z^2/2}$$

$$P[f(x) \ge z] \le e^{-cz+{\frac{c^2}{2}}$$

2. Relevant equations

$$P[\left|f(x)\right| \ge z] \le \frac{1}{z^2}$$

3. The attempt at a solution

The first thing to do is to set the function in the Probability constraint to the absolute value

$$P[\left|f(x)\right| \ge z] \le 2.e^{-cz+{\frac{c^2}{2}}$$

$$P[\left|f(x)\right| \ge z] \le 2.e^{-cz}.e^{\frac{c^2}{2}}$$

At the point I get confused. If $$e^{-cz}$$ is 1=> c or z must be zero. Any idea how to proceed?