Implementing a multiplexer for a given function
Here's a hint: draw up the truth table and think about the multiplexer as a look up table. I.e. choose two of the inputs (A,B,C) to act as the select inputs of the multiplexer, it doesn't matter which ones. Then basically we just have to look at how the output depends on the third input.

Say we select A and B to be the multiplexer control inputs. For each of the four possible combinations of A and B they will select a different input, or 'look up' the output value. Now you just have to look at how the output depends on C.

So for example when A and B are both zero the first input will be routed to the output. For the logic function you gave, the output will be 1 if C is 0 and 0 if C is 1. Basically this means the first mux input should be connected to NOT C as this will produce the desired output.

Similarly, for A=0, B=1 the second input is selected. In the case of the logic function you gave, the output is always 1 regardless of the value of C so the second mux input should be just connected to a high voltage.

You can continue with this process to determine what the other inputs should be connected to. 

To summarise the procedure is:

-Choose two inputs to control the mux

-For each of the four control input combinations, look how the output depends on the third input. The only possibilities here are C, !C, always 1 or always 0.

-Connect the appropriate mux input up to the appropriate possibility. 

This may be somewhat unclear without a logic diagram, but I have left that out intentionally so you can work through it. It is a rewarding process.