Suppose `f_1a n df_2` are non=zero one-one functions from `RtoRdot` is `(f_1)/(f_2)` necessarily one-one? Justify your answer. Here, `(f_1)/(f_2): RvecR` is given by `((f_1)/(f_2))(x)=(f_1(x))/(f_2(x))` for all `xRdot`

Explanation

We know that `f_{1} ; R arrow R,` given by` f_{1}(x)=x^{3} and f_{2}(x)=x` are one-one.

Injectivity of `f_{1} :`
Let` x` and` y` be two elements in the domain` R,` such that

`f_{1}(x)=f_{2}(y) Rightarrow x^{3}=y Rightarrow x=3 sqrt{y} in R`

So, `f_{1} `is one-one.

Injectivity of `f_{2}` :

Let` x `and `y` be two elements in the domain `R `such that


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