Question

Given ( f(x) = x(x - 1) ) and ( g(x) = 3x ), find ( f ∘ (f ⋅ g)(6) ).

a) 360
b) 312
c) 96
d) 72

Answer 1

To find f ∘ (f ⋅ g)(6), calculate f ⋅ g and substitute the value of 6 into the resulting function to get 918.

Step-by-step explanation:

We are given f(x) = x(x - 1) and g(x) = 3x. To find f ∘ (f ⋅ g)(6), we need to first calculate f ⋅ g and then substitute the value of 6 into the resulting function.

f ⋅ g(x) = f(g(x)) = f(3x) = (3x)((3x) - 1) = 9x(3x - 1) = 27x² - 9x.

Now, we can substitute 6 into f ⋅ g(x) to find the final result. f ∘ (f ⋅ g)(6) = 27(6)² - 9(6) = 27(36) - 54 = 972 - 54 = 918. Therefore, the correct answer is 918.