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Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 5 Maths Textbook Solution.

Answers (1)

Answer:              

f^{-1}\left ( x \right )=\frac{x-5}{3} 

Given:

f:Q\rightarrow Q, defined by f\left ( x \right )= 3x+5

Hint:

Solution:

Injectivity of f:

Let x and y be two elements of the domain\left ( Q \right ), such that,

f\left ( x \right )= f\left ( y \right )

3x+5=3y+5

                3x=3y

                x=y

So, f is one-one.

Subjectivity of f

Let  y be n the codomain\left ( Q \right ), f\left ( x \right )=y.

                3x+5=y

                3x=y-5

                x=\frac{y-5}{3}

f is onto.

So, f is bijection.

Let          f^{-1}\left ( x \right )=y                                                                                                                                       …(i)

x =f\left ( y \right )

x=3y+5

x-5=3y

y=\frac{x-5}{3}

f^{-1}\left ( x \right )= \frac{x-5}{3}                                                                                                                                [From (i)]            

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