Mark (√) against the correct answer in the following:

Question:

Mark (√) against the correct answer in the following:

If $f(x)=\frac{(4 x+3)}{(6 x-4)}, x \neq \frac{2}{3}$ then $(f$ of $f(x)=?$

A. $\mathrm{X}$

B. $(2 x-3)$

C. $\frac{4 x-6}{3 x+4}$

D. None of these

 

Solution:

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

$\Rightarrow \mathrm{f}(\mathrm{f}(\mathrm{x}))=\frac{4 \mathrm{f}(\mathrm{x})+3}{6 \mathrm{f}(\mathrm{x})-4}=(\mathrm{f}$ of $\mathrm{f})(\mathrm{x})$

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

$\Rightarrow \mathrm{f}(\mathrm{f}(\mathrm{x}))=\frac{16 \mathrm{x}+12+18 \mathrm{x}-12}{24 \mathrm{x}+18-24 \mathrm{x}+16}=\frac{34 \mathrm{x}}{34}=\mathrm{x}$

 

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