Monotonicity Then Counting

★ 7/10functions calculus Monotonicity AM-GM

Problem

Let

f(x) = \ln x + \frac{a}{x+1},

and suppose $f(x)$ is increasing on its domain. Discuss the number of solutions of the equation

f(x) = x^2 - 2x + 3.

Answer

Solution

Difficulty	7/10
Topics	functions, calculus, Monotonicity, AM-GM

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