Question

l3-4xl>=9 find the domain and range

Answer 1

Answer:

Step-by-step explanation:

According to definition of absolute value:

|x| = x , if x ≥ 0 ("x" is positive or 0) and

|x| = - x , if x < 0 ("x" is negative)

1). Assume the value of expression (3 - 4x) is positive or zero, then

3 - 4x ≥ 9

- 4x ≥ 9 - 3 = 6  

x ≤ 6 ÷ (- 4)

x ≤ - 1.5 , x ∈ (- ∞ , - 1.5]

2). Assume the value of expression (3 - 4x) is negative, then

- (3 - 4x) ≥ 9

3 - 4x ≤ - 9

- 4x ≤ - 12

x ≥ 3 , x ∈ [3 , ∞)

Thus, domain is ( - ∞, - 1.5] ∪ [3, ∞)

f(x) = |3 - 4x| - 9 ≥ 0

Thus, range is [0 , ∞)