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Show that if f1a n df1 are one-one ma...

Show that if `f_1a n df_1` are one-one maps from `RtoR ,` then the product `f_1xf_2: RvecR` defined by `(f_1xf_2)(x)=f_1(x)f_2(x)` need not be one-one.

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We know that` f_{1}: R -> R`, given by `f_{1}(x)=x_{r} and f_{2}(x)=x `are one-one.
Proving` f_{1}` is one-one:
Let `x` and `y` be two elements in the domain `R`, such that
`f_{1}(x)=f_{1}(y) `
`Rightarrow x=y`
So, `f_{1}` is one-one.
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