You might want to break up the situation under g < a or g > b (for three) and show whether its possible to get f + g in [a,b].
true or false,if true give proofs, false then find exampleR[a,b] is defined
the regulated function on [a,b])
(a) f∉ R[a,b] implies |f|∉ R[a.b]
R[a,b] implies f∉ R[a,b]
(c)f∈R[a.b], g∉ R[a,b] imply f+g ∉R[a,b]
i do need some helps in 3 statement cause i dont know how to begin.