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Please solve RD Sharma class 12 Chapter Functions exercise 2.1 question 19 maths textbook solution.

Answers (1)


f_1 and f_2 are one-one mapping.

To prove:

The product f_1 \times f_2 is not one-one.


Let f_1:R\rightarrow R  be defined by f_1(x)=x

and      f_2:R\rightarrow R be defined by f_2(x)=x 

Clearly f_1 and f_2  are one-one functions.

Now,    F= f_1\times f_2:R\rightarrow R is defined by

            F(x)=\left(f_{1} \times f_{2}\right)(x)=f_{1}(x) \times f_{2}(x)=x^{2}                                                                         …(i)

Clearly F(-1)=1=F(1)

since the two elements have the same  image.

 \therefore Fis not one-one.    

Hence f_1 \times f_2 is not one-one.

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