Domain and range of the function g(x) = (6 - 4x)(square root)?

Question

Find the domain and range of the function g(x) = (6 - 4x) (square root).


a. Domain [-4,4], Range [2,∞)
b. Domain (-∞,3], Range [3,∞)
c. Domain (-∞,32] , Range [0, ∞)
d. Domain (-∞,3], Range [0,∞)
e. Domain [4,6], Range [0,∞)

Answer 1

Domain is(-∞,1.5]
Range is [0,∞)
are you sure answer c shouldnt be 3/2 = 1.5 instead of 32?

Answer 2

The main thing to remember for square roots is that whatever is under the square root has to be either 0 or positive. Start by setting the part under the square root as an inequality so that it's: 3x+6 >= 0 (is the 6 under the square root?) 3x >= -6 x >= -3 If the 6 isn't under the square root: 3x >= 0 x >= 0 That's the domain (whichever inequality it is from above) To find the range, plug in the lowest value in the domain (either -3 or 0). Because there is no - sign in front of the square root, it will only increase, so the range is from the y-value for either -3 or 0 on up.

Answer 3

c. Domain (-∞,3/2] , Range [0, ∞)
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Ideas: 6-4x ≧ 0 => x ≤ 3/2

Answer 4

%range(-4, 0)+domain of (i) inf.