The two polynomial functions g and h are defined by g(x)=5x6−4 and h(x)=−x3+2.
a. (i) Find the domain of each function.
b. (ii) Determine the range of each function, expressing your answers in interval notation.
c. (iii) Which of the two functions has the larger minimum value? Justify your answer.
d. (iv) State, with reasons, whether the value y=10 lies in the range of (a) g and (b) h.