# Inequalities of the Form $$f(g(x)) \geq f(x)$$

by Tal Kubo (Brookline High School)

This article originally appeared in:
Mathematics Magazine
December, 1990

Subject classification(s): Functions | Single Variable Calculus | Calculus | Inequalities | Algebra | Algebra and Number Theory
Applicable Course(s): 4.21 Senior Seminar / Independent Study in Math | 3.1 Mainstream Calculus I | 3.0 Calculus

The author finds a way of finding a function $$g$$ such that $$f(g(x)) \geq f(x)$$ and shows two applications of this method.

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Capsule Course Topic(s): One-Variable Calculus | Integration: Applications