Mathematics

Question

Find the domain and range for the absolute value function f(x)=| x+2 |-3

1 Answer

  • f(x) = |x + 2| - 3
       0 = |x + 2| - 3
       0 = x + 2 - 3
       0 = x - 1
    + 1      + 1
        1 = x

    Domain: x > 1 and x < 1
    Solution Set of the Domain: {x| 1 > x > 1} and {x|x 1 < x < 1} or (1, 1)

    f(x) = |x + 2| - 3
    f(x) = |0 + 2| - 3
    f(x) = |2| - 3
    f(x) = 2 - 3
    f(x) = -1

    Range: x ≤ 3
    Solution Set of the Range: {x|x ≤ 3} or (-∞, 3]