Consider the rational function

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

Problem

Consider the rational function f(x)=ax+bcx+df(x)=\dfrac{ax+b}{cx+d}, where ad−bc≠0ad-bc\neq 0 and cx+d≠0cx+d\neq 0 on the interval of interest. Which of the following gives (f−1)′(x)(f^{-1})'(x) in terms of the constants a, b, c, da,\,b,\,c,\,d and the variable xx? (a) ad−bc(cx+d)2\displaystyle \frac{ad-bc}{(cx+d)^{2}} (b) (−cx+a)2ad−bc\displaystyle \frac{(-cx+a)^{2}}{ad-bc} (c) ad−bc(−cx+a)2\displaystyle \frac{ad-bc}{(-cx+a)^{2}} (d) −(ad−bc)(cx+d)2\displaystyle \frac{-(ad-bc)}{(cx+d)^{2}}

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