Final answer:
The value of the composite function ((h)/(g))(-3), where h(x) = 5 - 4x² and g(x) = 7 - 3x, is -31/16 after evaluating h(-3) and g(-3) and dividing the two results.
Step-by-step explanation:
The student is asking for the evaluation of a composite function, specifically requesting the value of the function ((h)/(g))(-3) where h(x) = 5 - 4x² and g(x) = 7 - 3x. To find this value, we first evaluate both h(-3) and g(-3), and then divide the result of h(-3) by the result of g(-3). Starting with h(-3), we substitute -3 into h(x) which gives us h(-3) = 5 - 4(-3)² = 5 - 4(9) = 5 - 36 = -31. Next, we evaluate g(-3) by substituting -3 into g(x) resulting in g(-3) = 7 - 3(-3) = 7 + 9 = 16. To find ((h)/(g))(-3), we divide h(-3) by g(-3): ((h)/(g))(-3) = (-31) / 16. Therefore, the value of the given composite function at x = -3 is -31/16.