(a) If Ax=b has infinitely many solutions, then for any two solutions x_1 and x_2 we have A(x_1-x_2) = 0 and thereby Ax=0 has infinitely many solutions.
(b) That is not true, an easy example would be A=(0) and b arbitrary, but not zero.
(c) Assume, we have three or less hyperplanes intersecting...
There's a little mistake in there (no offense to Robert, just a slip that happens to all of us), in Part A we find
f(g(x)) = -g(x)+5 = -(4x+2)+5 = -4x+3
"Average" and "Mean" are normally two terms used for the same expression, namely the sum of all elements divided by their number. Using both of these terms is normally done to clarify which form of a mean we choose among quite a few options as there are
several other ways...