Show that the following functions belong to R*[0, 1] by finding a function Fk that is continuous on [0, 1] and such that Fʹk(x) = fk(x) for x ∈ [0, 1]\Ek, for some finite set Ek.
(a) f1(x) := (x + 1)/√x for x ∈ [0, 1] and f1(0) := 0.
(b) f2(x) := x/√1 - x for x ∈ [0, 1] and f2(1) := 0.
(c) f3(x) := √x ln x for x ∈ [0, 1] and f3(0) := 0.
(d) f4(x) := (ln x)/√x for x ∈ [0, 1] and f4(0) := 0.
(e) f5(x) := √(1 + x)/(1 - x) for x ∈ [0, 1] and f5(1) := 0.
(f) f6(x) := 1/√x√2 - x for x ∈ [0, 1] and f6(0) := 0.