Question

What is the domain and range of `f(x) = (x-1)/ (x^2 -x-6)`?

Answer 1

`D_f= [-oo,+oo], xnotin[-2],[3]`

`R_f= [-oo, +oo]`

Explanation:

Since we have a rational function, we know that we can't take values of `x` for which the denominator equals `0`. We also know that there will be asymptotes as these `x`-values, so the range of the function will be over the reals

`x^2-x-6=(x+2)(x-3)`

Thus `f` will have asymptotes at `x=3` and `x=-2`, so these aren't included in the domain. However, all other `x`-values are valid.