Give examples of two one-one functions `f_1` and `f_2` from `R` to `R` such that `f_1+f_2: R->R` , defined by `(f_1+f_2)(x)=f_1(x)+f_2(x)` is not one-one.

Explanation

As we know that `f_1:R->R`, given by `f_1(x)=x`, and `f_2(x)=−x` are one-one.

Now proof `f_1`is one-one :

Find `f_1(x_1):`

`impliesf_1(x_1)=x_1`

Find `f_1(x_2):`

`impliesf_1(x_2)=x_2`

​Let` f_1(x_1)=f_1(x_2)`

`implies x_1=x_2`

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