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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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