How to find the CDF of a transformation | Probability Theory

Let X be an exponential random variable with mean 1. Find the distribution of Y := (X − 1)+, where x+ = xI(0,∞)(x). We go about solving this by finding the CDF of the transformation of X.
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This question was taken from the University of Cape Town’s STA2004F (Statistical Theory and Inference) course with permission.
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