if the function f (x) has a domain of - 2≤x≤8 and a range of - 4≤y≤6 and the function g (x) is defined by the formula g (x) = 5f (2x) then what are the domain and range of g. explain your thought process

Domain: - 1 ≤ x ≤ 4

Range: - 20 ≤ 5f (2x) ≤ 30

Step-by-step explanation:

Inputs of f are between - 2 and 8

Input is now 2x, so

-2 ≤ 2x ≤ 8

-1 ≤ x ≤ 4

(Horizontal stretch, factor 1/2)

Range of f is - 4 ≤ y ≤ 6

So,

-20 ≤ 5y ≤ 30

(Vertical stretch, factor 5)