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

1 Answer
Aug 13, 2018

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

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(x3)(x+3)x3=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)