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

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

Answers (1)

Answer:

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.

Posted by

infoexpert27

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