While it is true that you can build logic gates using switch logic ... So you can do anything with a single mux except NAND, NOR, XOR, and XNOR, which each need two. Report comment.

This paper designs an 8:1 multiplexer with CMOS Transmission Gate Logic (TGL) using the power gating technique, which reduces the leakage power and leakage current in active mode.

The NAND gate is a circuit that outputs '0' when both inputs are '1', and '0' otherwise, so if you arrange the NAND gate as follows, the Invert circuit is completed.