Answer the following questions related to the idea of the domain of a real-valued function.
a. (i) Define the domain of a real-valued function.
b. (ii) For g(x)=3x−2, write the algebraic condition that x must satisfy and briefly explain why this condition is necessary.
c. (iii) For h(x)=x2−41, state the values of x that are excluded from the domain and give a reason for each exclusion.
d. (iv) For p(x)=log2(x+7), state the condition on x that ensures p(x) is defined and explain your reasoning.