A Monotone Exp-Log Difference

★ 7/10functions Extrema calculus Monotonicity Logarithms

Problem

The function

f(x) = a^{x-1} - \log_a(x - 1) \qquad (a > 0,\ a \neq 1)

is monotonic on its domain. Find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, calculus, Monotonicity, Logarithms

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