For , let , where is a constant. Given that and , determine the value of…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For x≠1x\neq 1, let f(x)=mx+2x−1f(x)=\dfrac{m x+2}{x-1}, where mm is a constant. Given that f(3)=1f(3)=1 and (f−1)′(1)=−2(f^{-1})'(1)=-2, determine the value of mm.

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