Find the domain and show steps.

Question

Find the domain of the function and show your steps.

f(x)=(x+12)/(x-5)

Answer 1

For the domain, there will be a break in the domain at the vertical assymptote. To find this, set the denominator equal to zero and solve.

x-5=0 Add 5 to both sides

x-5+5=0+5

x≠5

Domain: (-∞,5) U (5,∞)

Answer 2

The domain is the whole real line except for x=5.

In general rational functions are continuous except at zeroes of the denominator.