Question

The function f has domain [-2,2] and range [1,5]. The function g is given by g(x)=-2f(x+3)+4. What are the domain and range of g ?

A. domain: [-5,-1] , range: [-6,2]
B. domain: [-5,-1] , range: [-2,6]
C. domain: [1,5] , range: [-2,6]
D. domain: [1,5] , range: [-6,2]

Answer 1

The domain of g is [1,5] and the range of g is [-6,2].

Step-by-step explanation:

The function g(x) is given by g(x)=-2f(x+3)+4. To find the domain and range of g, we need to consider the domain and range of f. The given function f has a domain [-2,2] and a range [1,5]. When we substitute (x+3) into f, the new domain becomes [-2+3,2+3] = [1,5]. Therefore, the domain of g is also [1,5].

To find the range of g, we substitute the range of f into the formula for g. Since g(x)=-2f(x+3)+4, the new range becomes [-2(1)+4,-2(5)+4] = [2,-6]. Therefore, the range of g is [-6,2].