Question

find domain and range for y=√(9x-x^2 )

Answer 1

F(x) =
Clearly f(x) assumes real values , if
9 - x² ≥ 0
-x² + 9 ≥ 0
-( x² - 9 ≥ 0)
x² - 9 ≤ 0
(x-3)(x+3) ≤ 0
x {-3,3}
domain f(x) = {-3,3}
range,
let y = f(x)
y =
y² = 9 -x²
x² = 9-y²
x =
clearly , x will take real values , if
9 - y² ≥ 0
y² - 9 ≤ 0
(y-3)(y+3)≤ 0
-3≤y≤3
y {-3,3}
y = ≥ 0 for all x {-3,3}
y {0,3} for all x {-3,3}
hence, range (f) = {0,3}