how can you find the range and domain of root of (9-x2)?

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}

  • 33

Here, f(x) =√9-x²

Lets take, x = 1Then,√9-1² =√9-1 = √8x = 2Then,√9-2² = √9-4 =√5x = 3Then,√9-3² =√9-9 = 0x = 4Then,√9-4² =√9-16 =-√7and so on.Here, {1,2,3,4} = Domainand, {√8,√5,0,-√7} = RangeThis f(x) =√9-x² will have infinite number of elements or members of Domain and range.So, Domain = {-,}And, Range = {-,}
  • -24
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