Question

Domain for g(x) = √4x – x^2​

Answer 1

`\large\boxed{0\leq x\leq4\to x\in[0,\ 4]}`

Explanation:

We know: √x exist if x ≥ 0.

We have
`g(x)=√(4x-x^2)`.

The domain:

`4x-x^2\geq0\\\\x(4-x)\geq0`

Find the zeros of the equation

`x(4-x)=0\iff x=0\ or\ 4-x=0\\\\x=0\ or\ x=4`

`ax^2+bx+c=-x^2+4x\to a=-1<0`

the parabola open down.

Look at the picture.

`x\geq0\ \wedge\ x\leq4\to0\leq x\leq4\to x\in[0,\ 4]`

Answer 2

The domain is 0 ≤ x ≤ 4,

or in interval notation it is [0, 4].

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.