Problem #PRU-110122

Problems Algebra and arithmetic Algebraic inequalities and systems of inequalities Algebraic inequalities (other) Calculus Functions of one variable. Continuity Monotonicity, boundedness
 14–16  4.0

Problem

The functions \(f (x) - x\) and \(f (x^2) - x^6\) are defined for all positive \(x\) and increase. Prove that the function

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also increases for all positive \(x\).