Answer:
(-6,-5)=> f(x)= x^2-2x-5
(8,11)=> f(x)=3x+5
(3,2)=> f(x)=4-x
(6,28)=> f(x)=(x+5) x^2
Explanation:
For f(x)=3x+5
Putting the values of domain one by one:
Putting x=1:
f(x)=3(1)+5
=3+5
=8
Putting x = 2:
f(x)=3(2)+5
=6+5
=11
For function f(x)= x^2-2x-5
Putting x=1:
f(x)=〖(1)〗^2-2(1)-5
=1-2-5
= -6
Putting x=2
f(x)=〖(2)〗^2-2(2)-5
=4-4-5
= -5
For f(x)=(x+5) x^2
Putting x=1
f(x)=(1+5) (1)^2
=6*1
=6
Putting x=2
f(x)=(2+5) (2)^2
=7*4
=28
For f(x)=4-x
Putting x = 1
f(x)=4-1
=3
Putting x=2
f(x)=4-2
=2
So the ranges belonging to the functions when domain is (1,2) are:
(-6,-5)=> f(x)= x^2-2x-5
(8,11)=> f(x)=3x+5
(3,2)=> f(x)=4-x
(6,28)=> f(x)=(x+5) x^2