#### Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 8 Maths Textbook Solution.

$f$ is invertible.

Given:

$f\left ( x \right )=\frac{4x+3}{6x-4},x\neq \frac{2}{3}$

Hint:

If the function is invertible, $f\! o\! f=1$.

Solution:

$f\left ( x \right )=\frac{4x+3}{6x-4},x\neq \frac{2}{3}$

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

$\frac{4\left ( \frac{4x+3}{6x-4} \right )+3}{6\left ( \frac{4x+3}{6x-4}\right )-4}=\frac{16x+12+18x-12}{24x+18-24x+16}=\frac{34x}{34}=x$

$\therefore f\! o\! f\left ( x \right )=x$ for all $x\neq \frac{2}{3}$

$f\! o\! f=1$

Hence, the given function $f$ is invertible and inverse of $f$ is $f$ itself.