Question

Let f be a function such that f(x)=2x-4 is defined on the domain.2 is less than or equal to x and x is lss than or equal to 6. The range of the function

Answer 1

F(x) = 2x - 4
f(2 ≤ x) = 2(2 ≤ x) - 4
f(x ≥ 2) = 2(x ≥ 2) - 4
f(x ≥ 2) = 2(x) ≥ 2(2) - 4
f(x ≥ 2) = 2x ≥ 4 - 4
f(x ≥ 2) = 2x ≥ 0
f(x ≥ 2) = x ≥ 0

f(x) = 2x - 4
f(x ≤ 6) = 2(x ≤ 6) - 4
f(x ≤ 6) = 2(x) ≤ 2(6) - 4
f(x ≤ 6) = 2x ≤ 12 - 4
f(x ≤ 6) = 2x ≤ 8
f(x ≤ 6) = x ≤ 4

Answer 2

The range of the function is the set of values it can achieve.  The minimum value plugs in 2 to get 2*2-4, or 0.  The maximum value uses 6, and is 6*6-4, or 8.  Thus, the range is 0 to 8, inclusive.