Question

Part 1: Composition of Functions

1. Given S(x)= 3x - 4 and g(x)=-2x+7 evaluate:
(a) f(g(0))
(b) 8(f(-2))
(c) f(f(3))
(d) (gºf)(6)
(e) (f•g)(5)
(f) (8°8)(2)
please explain how you got your answers, thanks!

Answer 1

The composition of functions and individual function evaluations involve the application of one function into another and then performing arithmetic operations as required. The evaluated values based on the provided functions S(x) and g(x) are 17, -80, 11, -21, and -13 for the respective parts of the question.

Step-by-step explanation:

The question involves the composition of functions and evaluating functions at given values. Let's solve each part step by step:

1. f(g(0)): To find this, we first evaluate g at 0. Since there was a typo, I'm assuming f(x) = S(x) for consistency. g(0) = -2(0) + 7 = 7. Now, f(g(0)) = f(7) = 3(7) - 4 = 21 - 4 = 17.
2. 8(f(-2)): This requires evaluating f at -2 then multiplying by 8. f(-2) = 3(-2) - 4 = -6 - 4 = -10. So, 8(f(-2)) = 8(-10) = -80.
3. f(f(3)): Here, we first find f(3), then evaluate f at that result. f(3) = 3(3) - 4 = 9 - 4 = 5. Then, f(f(3)) = f(5) = 3(5) - 4 = 15 - 4 = 11.
4. (g°f)(6): This is the composition of g after f, evaluated at 6. First find f(6), then apply g. f(6) = 3(6) - 4 = 18 - 4 = 14. g(f(6)) = g(14) = -2(14) + 7 = -28 + 7 = -21.
5. (f•g)(5): This is the composition of f after g, evaluated at 5. First find g(5), then apply f. g(5) = -2(5) + 7 = -10 + 7 = -3. f(g(5)) = f(-3) = 3(-3) - 4 = -9 - 4 = -13.
6. Since there might be a typo in (8°8)(2), and the function '8' is not defined, this part cannot be evaluated with the given information.