Define the function
h(x)=5−2x+x2−4x+31.
(i) Obtain the inequality that must be satisfied for the first square-root term to be real.
(ii) Obtain the pair of conditions that make the second term real and finite.
(iii) Solve the inequalities found in parts (i) and (ii), and clearly identify any points that must be excluded.
(iv) Hence determine the domain of h(x), expressing your answer on a number line or in interval notation.