Answer the following with respect to the concept of domain of a real-valued function:
a. (i) Define the domain of a function.
b. (ii) Explain, with reason, why the domain of f(x)=x−31 excludes the value x=3.
c. (iii) For g(x)=5−2x, state the inequality that x must satisfy so that g(x) is real and explain your reasoning.
d. (iv) Justify why the expression log10(x+4) imposes a different kind of restriction on x compared to the restrictions in parts (ii) and (iii).