That is now question, stupid!
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The INVERSE of any relation is obtained by switching the coordinates in each ordered pair.
Where f(x) = lambda* exp(-lambda*x), Inverse cumulative distribution= -ln(1-p)/lambda. See http://en.wikipedia.org/wiki/Exponential_distribution Note that if used in random number generation, with "x" equal to the random deviate, then given U ~ uniform(0,1), then x = -ln(U)/lambda.
Disadvantages: 1. requires a closed form expression for F(x) 2. speed ... often very slow because a number of comparisons required Advantages: Inverse transform method preserves monotonicity and correlation which helps in 1. Variance reduction methods ... 2. Generating truncated distributions ... 3. Order statistics ...
Well, it's a non-linear relationship. It could be inverse, or quadratic, or many other things.