If f(x)


If $f(x)=\frac{4 x+3}{6 x-4}, x \neq \frac{2}{3}$, show that $f \circ f(x)=x$ for all $x \neq \frac{2}{3}$. What is the inverse of $f$ ?


$(f o f)(x)=f(f(x))$

$=f\left(\frac{4 x+3}{6 x-4}\right)$

$=\frac{4\left(\frac{4 x+3}{6 x-4}\right)+3}{6\left(\frac{4 x+3}{6 x-4}\right)-4}$

$=\frac{16 x+12+18 x-12}{24 x+18-24 x+16}$

$=\frac{34 x}{34}$


$\Rightarrow(f o f)(x)=x=I_{X}$, where $I$ is an identity function.

So, $f=f^{-1}$

Hence, $f^{-1}=\frac{4 x+3}{6 x-4}$

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