Inverses of a quartic 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).
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