Find domain and range of f(x)=x²-9/x-3?

1 Answer
Aug 13, 2018

Answer:

Domain: #(- oo,3)uu(3, +oo)#
Range: #(-oo,6)uu(6, +oo)#

Explanation:

If you factor the numerator, you can see that you will have terms that cancel out:

#((x-3)(x+3))/(x-3)=x+3#

#therefore# #f(x)=x+3# with a hole at #x=3#

So the domain is all real numbers except for #x=3# aka #(-oo,3)uu(3, +oo)#

Plug in three for #x# to find out where the range doesn't exist:

#y=6#

So, the range is all real numbers except for #y=6# aka #(-oo,6)uu(6, +oo)#