My textbook has the following introductory example about functions of random variables:
Suppose that $X$ is a random continuous variable with a uniform distribution over the interval $(0,1)$. Determine the distribution of $Y = aX + b$, where $a$ and $b$ are non-zero integers.
The solution provided in the textbook comes with no explanation and it differs from what I ended up with. What's the correct way to solve this problem?