Question

For a given function `f(x)=x^a/x^b`, is it correct to say that `f(0)=0,1or"undefined"` depending on the values of `a` and `b`?

For example, take `f(x)=x^2/x^2`, we can just simplify this to `f(x)=1`, and say `f(0)=1`, however we can also say that `f(0)=0^2/0^2=0/0="undefined"`

Or, with `f(x)=x^2/x`, we can simplify this to `f(x)=x` and so `f(0)=0`. However, we can also make it so `f(0)=0^2/0="undefined"`.

Answer 1

Consider that:

`f(x) =x^a/x^b = x^(a-b) =x^c`

with `c=a-b`. So:

`a=b => c=0 => f(0) = 1`

`a > b => c > 0 => f(0) = 0`

`a < b => c < 0 => f(0)` is undefined