The function $$$\mathrm{f}$$$ is defined by $$$\mathrm{f}(x)=\frac{2 x}{3 x-1}$$$ for $$$x>\frac{1}{3}$$$. Find an expression for $$$\mathrm{f}^{-1}(x)$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_13 Year：2020 Question No：6(a)

Answer:

$y=\frac{2 x}{3 x-1} \rightarrow 3 x y-y=2 x \rightarrow 3 x y-2 x=y($ or $-y=2 x-3 x y)$
$x(3 y-2)=y \rightarrow x=\frac{y}{3 y-2} \quad\left(\right.$ or $\left.x=\frac{-y}{2-3 y}\right)$
$\left(f^{-1}(x)\right)=\frac{x}{3 x-2}$

Knowledge points:

1.2.3 determine whether or not a given function is one-one, and find the inverse of a one-one function in simple cases

Answer:

Knowledge points:

Solution:

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