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Please solve RD Sharma class 12 Chapter Functions exercise 2.1 question 17 maths textbook solution.

Answers (1)

Let $f_1:R\rightarrow R$ and $f_2:R\rightarrow R$ be two function given by

$f_1(x)=x$

$f_2(x)=x$

We can easily verify that $f_1$ and $f_2$ are one-one functions.

Now,

$\left(f_{1}+f_{2}\right) x=f_{1}(x)+f_{2}(x)=x-x=0$

$\therefore f_1+f_2:R\rightarrow R$ is a function given by $(f_1+f_2)x=0$

Since $f_1+f_2$ is a constant function.

Hence it is not one-one.

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