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

1 Answer
Jun 6, 2017

Answer:

#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.