Question

find the range of the function f(x)=x2-6x.

If the domain is(-7,-2,1)

Answer 1

Hello :
1)  x²-6x = -2
x²-6x+2=0
x²-2(3)x+9-9+2 =0
(x-3)² -7 = 0
(x-3)²=(√7)²
 x-3 =√7   or x-3 = - √2
x=3+√2    or x= 3-√2

2)  x²-6x = -7
x²-6x+7=0
x²-2(3)x+9-9+7 =0
(x-3)² -7 = 0
(x-3)²=(√7)²
 x-3 =√7   or x-3 = - √7
x=3+√7    or x= 3-√7
3 )

  x²-6x = 1
x²-6x-1=0
x²-2(3)x+9-9-1 =0
(x-3)² -10 = 0
(x-3)²=(√10)²
 x-3 = √10 or x-3 = - √10
x=3+ √10   or x= 3- √10
the range is : {3+√2,3-√2 ,3+√7,3-√7 ,3+ √10  , 3- √10 }