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Please Solve RD Sharma Class 12 Chapter Function Exercise 2.4 Question 6 Maths Textbook Solution.

Answers (1)

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Answer:

$f^{-1}\left ( x \right )=\frac{x-3}{4}$

Given:

$f\left ( x \right )=4x+3,f:R\rightarrow R$ .

Hint:

Bijection function should be fulfil the injectivity, surjectivity.

Solution:

Let $x,y$ be two elements of domain $\left ( R \right )$ , such that

$4x+3=4y+3$

$4x=4y$

$x=y$

So, $f$ is one-one.

Let $y$ be in the co-domain $\left ( R \right )$ , such that $f\left ( x \right )=y$ .

$4x+3=y$

$4x=y-3$

$x=\frac{y-3}{4}\: \epsilon\: R$

$f$ is onto.

So, $f$ is a bijection.

$f^{-1}\left ( x \right )=y$ … (i)

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

$x=4y+3$

$x-3=4y$

$y=\frac{x-3}{4}$

$f^{-1}\left ( x \right )=\frac{x-3}{4}$

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