Question

The function, f(x), describes the height of a dome on top of a building, where f(x) is the height from the base of the dome and x is the horizontal distance from where the dome meets the building.f(x)=2√-x^2+10x

Answer 1

The given function is

$f(x)=2\sqrt[]{-x^2+10x}$

Domain is the set of all the possible values of x, i.e domain is the input of the function

Since The x must have the value that define the function properly

SInce, x is the horizontal distance, so, x will not be negative

Thus, the x has positive real number

For the Domain of F(x)

Equate the function with zero

$\begin{gathered} 2\sqrt[]{-x^2+10x}=0 \\ \sqrt[]{-x^2+10x}=0 \end{gathered}$

Squaring both side

$\begin{gathered} -x^2+10x=0 \\ -x+10=0 \\ x=10 \end{gathered}$

Thus, the value of x should not be greater than 10

Domain of the function is

$0\leq x\leq10$