Suppose `f_1` and `f_2` are non-zero one-one functions from `R` to `R` . Is `(f_1)/(f_2)` necessarily one-one? Justify your answer. Here, `(f_1)/(f_2): R->R` is given by `((f_1)/(f_2))(x)=(f_1(x))/(f_2(x))` for all `x in R` .

Explanation

As we know that `f_1:R->R`, given by `f_1(x)=x^3` and `f_2(x)=x` are one-one.

one−one test for `f_1:`

So, let `x_1` and `x_2`
be two elements in the domain R, such that,

`f_1(x_1)=f_2(x_2)`

Find `f_1(x_1):`

`impliesf_1(x_1)=(x_1)^3`

Find `f_2(x_2):`

...