Let f:D→R and g:D→R be functions with D nonempty, α∈R, and recall what f+g and αf means from the previous exercise.
a) Prove that if f+g and g are bounded, then f is bounded.
b) Find an example where f and g are both unbounded, but f+g is bounded.
c) Prove that if f is bounded but g is unbounded, then f+g is unbounded.
d) Find an example where f is unbounded but αf is bounded.