Final answer:
The composition (f ∘ g)(6) of the given functions f(x) and g(x) equals 16986 when evaluated step by step.
Step-by-step explanation:
To find the composition of functions (f ∘ g)(x), also written as f(g(x)), we first evaluate g(x) and then use that result as the input for f(x). Following this, we calculate g(6) and then f(g(6)).
The given functions are f(x) = 12x² - 9x and g(x) = 8x - 10. Let's find g(6) first:
- g(6) = 8(6) - 10 = 48 - 10 = 38
Now we compute f(g(6)) or f(38):
- f(38) = 12(38²) - 9(38)
- f(38) = 12(1444) - 9(38)
- f(38) = 17328 - 342
- f(38) = 16986
Therefore, the composition (f ∘ g)(6) is 16986.
Complete Question:
For the given functions f and g, find the indicated composition.
1.) f(x)= 12x^2 - 9x, g(x)= 8x-10
(f.g)(6)