Implementing 3 variable boolean function using mux 4 to 1 and inverter
It is possible to make any boolean function
f(a,b,c) using a 4:1 mux and an inverter

With the inverter make ~c

Connect a and b to the mux address lines.

Connect each mux data input to the one of 0,1,c,or ~c as appropriate.

The mux output has your function result.