6. (8%) Let X and Y be two random variables. X has the p.d.f. $f_X(x) = 2x, 0 \le x \le 1$, and Y = g(X). If Y has the p.d.f. $f_Y(y) = e^{-y}, y > 0$, find the function g(x).
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6. (8%) Let X and Y be two random variables. X has the p.d.f. $f_X(x) = 2x, 0 \le x \le 1$, and Y = g(X). If Y has the p.d.f. $f_Y(y) = e^{-y}, y > 0$, find the function g(x).