Piecewise functions — computing a preimage set

Suppose $f$ is a function defined by

$$f(x)=\begin{cases}x & 0<x\le\frac12\ x-\frac12 & \frac12<x<1\end{cases}.$$

If $M=\left(\frac14,\frac12\right)$, $N=\left(\frac34,1\right)$ and $Q=\{x\mid f(x)\in(\frac14,\frac12)\}$, then which of the following is true?