Final answer:
To solve the function composition practice problems, we calculate f(g(x)) and g(f(x)) using the provided equations, resulting in -6x^2 + 31 and 18x^2 - 84x + 90, respectively. These can also be calculated using a graphing calculator like the TI-83, 83+, or 84 series.
Step-by-step explanation:
To solve the given practice problems, we need to perform function composition. The first task is to find f(g(x)), which means we will plug the function g(x) into f(x). The second task is g(f(x)), where we plug f(x) into g(x).
Solution A: Step-by-step calculation
1. f(g(x)): Apply g(x) = 2x2 - 8 into f(x) = -3x + 7.
So, f(g(x)) = -3(2x2 - 8) + 7 = -6x2 + 24 + 7 = -6x2 + 31.
2. g(f(x)): Apply f(x) = -3x + 7 into g(x) = 2x2 - 8.
So, g(f(x)) = 2(-3x + 7)2 - 8. This would be expanded and further simplified to
2(9x2 - 42x + 49) - 8 = 18x2 - 84x + 98 - 8 = 18x2 - 84x + 90.
Solution B: Using a TI-83, 83+, or 84 calculator
You can input the functions f(x) and g(x) into a TI calculator and use the built-in function composition feature to calculate f(g(x)) and g(f(x)). Ensure you check that the results are reasonable by comparing them to the step-by-step solution if possible.