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

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

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

It is given that $f(x)=(4 x+3) /(6 x-4), x \neq 2 / 3$

Now we have to show $\operatorname{fof}(x)=x$

$($ fof $)(x)=f(f(x))$

$=f((4 x+3) /(6 x-4))$

$=(4((4 x+3) /(6 x-4))+3) /(6((4 x+3) /(6 x-4))-4)$

$=(16 x+12+18 x-12) /(24 x+18-24 x+16)$

$=(34 x) /(34)$

$=\mathrm{x}$

Therefore, fof $(x)=x$ for all $x \neq 2 / 3$

\section{RD Sharma Solutions for Class 12 Maths Chapter 2 Function}

\Rightarrow \text { fof }=1

Hence, the given function $\mathrm{f}$ is invertible and the inverse of $\mathrm{f}$ is $\mathrm{f}$ itself.

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