For the function h(x)=logx+3(x2−4x+3), answer the following.
a. (i) Obtain all inequalities that x must satisfy so that both the base and the argument of the logarithm are valid.
b. (ii) Solve these inequalities simultaneously and hence write the domain of h.
c. (iii) Represent the domain on a number line, clearly indicating open and closed intervals.