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

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

Answers (1)

Given:

f_1 and f_2 are one-one mapping.

To prove:

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

Solution:

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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