Question

Given the function g(x) = 2x + 1. Find the domain using the range.
R:{-3, 1}
D:{ }

Answer 1

D = {-2, 0}

Explanation:

If the range is {-3, 1}, that means -3 and 1 are images of some points a, b in the domain. So, there are two points a, b in the domain such that:

g(a) = -3 and g(b) = 1

If g(a) = -3 then 2a + 1 = -3 ------>2a = -4 ------> a = -2

If g(b) = 1 then 2b + 1 = 1 ------> 2b = 0 ------> b = 0

Hence D = {-2, 0}