Solution
= Solution
Translate the inequality inside the <cumulative distribution function>:
$$
F_Y(y)=\mathbb P(1+X\leq y)=\mathbb P(X\leq y-1)=\boxed{F_X(y-1)}.
$$
Differentiating with the <chain rule> gives the <probability density function>
$$
\boxed{f_Y(y)=f_X(y-1)}
$$
almost everywhere. Translation shifts the <probability distribution> without changing its shape or its total probability.