Answer:
A. -77 < f(x) < -2
Step-by-step explanation:
- 4 < x < -1 so : (-1)² < x² < (-4)² because f is decrasing if - 4 < x < -1
1< x² < 16.....now multiply by : -5
-80 < - 5x² < -5 add 3 you have : -77< - 5x²+3 < -2
-77 < f(x) < -2
The range of function is -77 < f(x) < -2.
The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function.
Given function
f(x) = [tex]-5x^{2} +3[/tex]
Domain -4 < x < -1
If in the domain , x ⇒ small, f(x) ⇒ small
Maximum x =-1, f(x) = [tex]-5x^{2} +3[/tex]
f(x) = [tex]-5(-1)^{2} +3=-2[/tex]
Minimum x = -4
f(x) = [tex]-5(-4)^{2} +3=-77[/tex]
-77 < f(x) < -2
The range of function is -77 < f(x) < -2.
Find out more information about domain and range of a function here
brainly.com/question/20207421
#SPJ2
