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

1 Answer
Monzur R.
Jun 6, 2017

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.

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