Just got out of my stats final. Question.

Suppose $\displaystyle Z\sim -\frac{1}{h}e^{-\frac{z}{h}}.$

How do I find the MGF, $\displaystyle M_{\frac{1}{Z}}?$

Do I have to transform $\displaystyle Z,$ then use the definition of MGF? Or, is there some slick trick I'm missing here?