What is the domain if the range is {-4,-2,0}?

Question

Problem:

m(x)=4x+2

Range:{-4,-2,0}

Domain:?

Answer 1

The domain of a function is the set of valid input values, x. The range is the output values, m(x).

Since we are given the range {-4, -2, 0}, these are the valid output values, or m(x) = 4x + 2

Let's solve for x one by one:

m(x) = -4 = 4x + 2 (add -2 to both sides)

-6 = 4x (divide both sides by 4)

x = -3/2

m(x) = -2 = 4x + 2 (add -2 to both sides)

-4 = 4x (divide both sides by 4)

x = -1

m(x) = 0 = 4x + 2 (add -2 to both sides)

-2 = 4x (divide both sides by 4)

x = -1/2

Then domain is {-3/2, -1, -1/2}