Answer:
Domain is all real numbers except 4.
Range is all real numbers except 2.
Explanation:
You can find the domain by taking the denominator and setting it equal to 0 and then solving for x.
x-4=0
Add 4 to both sides
x=4
So, x cannot equal 4 in the domain.
You can find the range by using the inverse of the function, which means you flip the x and y.
x=2-5/(y-4)
Then you have to solve for y. Start by subtracting 2 from both sides.
x-2=-5/(y-4)
Multiply (y-4) to both sides.
(x-2)(y-4)=-5
Then divide (x-2) from both sides.
y-4=-5/(x-2)
Add 4 to both sides.
y=4-5/(x-2)
Then do the same as the domain and take the denominator and set it equal to 0 and solve for x.
x-2=0
Add 2 to both sides.
x=2
So the range cannot equal 2.