Answer: f(x)=(x-7)(x-4) for x<=4 or x>=7
f(x)=-(x-7)(x-4) for 4<x<7
Explanation:
|x^2-11x+28|=
|x^2-4x-7x+28|=
|x(x-4)-7(x-4)|=|(x-7)(x-4)|
f(x)=(x-7)(x-4) for x-4<=0 or x-7>=0 ==> both x-4 and x-7 have to be negative/positive in order for f(x) to be positive.
f(x)=-(x-7)(x-4) for x-4>0 and x-7<0 ==> Only x-4 or x-7 have to be positive in oder for f(x) to be positive.
f(x)=(x-7)(x-4) for x<=4 or x>=7
f(x)=-(x-7)(x-4) for x>4 and x<7
f(x)=(x-7)(x-4) for x<=4 or x>=7
f(x)=-(x-7)(x-4) for 4<x<7