Suppose $X$ follows a Uniform(4, 5) with CDF $$F_X(x) = \begin{cases} 1, & x \ge 5 \\ x-4, & 4 < x < 5 \\ 0, & x \le 4 \end{cases}.$$
Is the correct inverse of the above CDF the following? $$F_{X}^{-1}(u) = \begin{cases} 1, & u \ge 5 \\ u+4, & 4 < u < 5 \\ 0, & u \le 4 \end{cases}.$$