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Please solve RD Sharma class 12 Chapter Functions exercise 2.1 question 20 maths textbook solution.

Answers (1)

Let $f_1:R\rightarrow R$ and $f_2:R\rightarrow R$ are two function defined by $f_1(x)=x^2$ and $f_2(x)=x$ .

Clearly $f_1$ and $f_2$ are one-one functions.

Now, $\frac{f_1}{f_2}:R\rightarrow R$ given by

$\left(\frac{f_{1}}{f_{2}}\right) x=\frac{f_{1}(x)}{f_{2}(x)}=x^{2} \vee x \in R$

Let $\frac{f_1}{f_2}=f$

$\therefore f= R\rightarrow R$ defined by $f(x)=x^2$

Now, $f(-1)=1=f(1)$

since, the two elements have the same image.

$\therefore f$ is not one-one.

Hence, $\frac{f_1}{f_2}:R\rightarrow R$ is not one-one.

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