Determine the image of the function f(x)=x^2-6x+5 for x>=4

f(x) = x^2-6x+5.

To determine
the image of the function for x> 4..

f(x) =
x^2-6x+5.

f(x) = x^2-5x
-x+5.

f() =
x(x-5)-1(x-5).

Threfore f(x) =
(x-1)(x-5).

f(x) is a continous
funtion.

Therefore the image f(x) < 0 for x
belonging to  the interval (1,5) and   f(x) > 0, when x < 1, Or when
x>5.

Therefore  the image f(x) < 0  for   4
=< x < 5  , f(x) < 0.

The image f(x) =
0 when x =5.

And f(x) > 0 , for x >
5.

  x      f(x) = (x-1)(x-5)=
x^2-6x+5.

 4           -3

 
4.5       -1.75,

   
5          0

  
5.5       2.25

    6          5.