Consider the quartic polynomial y = f(x) = x⁴ - x².

a. Graph f and estimate the largest intervals on which it is one-to- one. The goal is to find the inverse function on each of these intervals.

b. Make the substitution u = x² to solve the equation y = f(x) for x in terms of y. Be sure you have included all possible solutions.

c. Write each inverse function in the form y = f^-1(x) for each of the intervals found in part (a).