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

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

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)]