Question

The zeros of a function `f(x)` are 3 and 4, while the zeros of a second function `g(x)` are 3 and 7. What are the zero(s) of the function `y=f(x)/g(x)?`

Answer 1

Only zero of `y=f(x)/g(x)` is `4`.

Explanation:

As zeros of a function `f(x)` are `3` and `4`, this means `(x-3)` and `(x-4)` are factors of #f(x).

Further, zeros of a second function `g(x)` are `3` and `7`, which means `(x-3)` and `(x-7)` are factors of #f(x).

This means in the function `y=f(x)/g(x)`, although `(x-3)` should cancel out

the denominator `g(x)=0` is not defined, when `x=3`. It is also not defined when `x=7`.

Hence, we have a hole at `x=3`.

and only zero of `y=f(x)/g(x)` is `4`.