Domain for g(x) = √4x – x^2
2 answers:
Answer:
![\large\boxed{0\leq x\leq4\to x\in[0,\ 4]}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B0%5Cleq%20x%5Cleq4%5Cto%20x%5Cin%5B0%2C%5C%204%5D%7D)
Step-by-step explanation:
We know: √x exist if x ≥ 0.
We have
.
The domain:

Find the zeros of the equation


the parabola open down.
Look at the picture.
![x\geq0\ \wedge\ x\leq4\to0\leq x\leq4\to x\in[0,\ 4]](https://tex.z-dn.net/?f=x%5Cgeq0%5C%20%5Cwedge%5C%20x%5Cleq4%5Cto0%5Cleq%20x%5Cleq4%5Cto%20x%5Cin%5B0%2C%5C%204%5D)
Answer:
The domain is 0 ≤ x ≤ 4,
or in interval notation it is [0, 4].
Step-by-step explanation:
g(x) = √(4x – x^2)
4x - x^2 cannot have a negative value because of the square root sign.
4x - x^2 = 0
x(4 - x) = 0
x = 0 , 4.
The highest value is 4 and the lowest is 0 . Values in between like 1 are in the domain ( for example √(4(1) - 1) = √3).
x has to be between 0 and 4 inclusive.
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