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

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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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