Roots of a Piecewise Absolute Equation

★ 7/10functionsAbsolute ValueMonotonicityalgebraCasework

Problem

Discuss the number of roots of the equation

∣x+1x∣−∣x−1x∣=kx+1\left|x+\frac 1x\right|-\left|x-\frac 1x\right|=kx+1

in terms of the real parameter kk.

Answer

Solution

Difficulty7/10
Topicsfunctions, Absolute Value, Monotonicity, algebra, Casework

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