Show that if `f_1` and `f_2` are one-one maps from `R` to `R` , then the product `f_1xxf_2: R->R` defined by `(f_1xxf_2)(x)=f_1(x)f_2(x)` need not be 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`

Now let `f_1(x_1)=f_1(x_2)`

`impliesx_1=x_2`

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