Final answer:
To find (f o g)(x), plug g(x) into f(x) and simplify. The domain of (f o g)(x) is all real numbers. To find (g o f)(x), plug f(x) into g(x) and simplify. The domain of (g o f)(x) is all real numbers.
Step-by-step explanation:
To find (f o g)(x), we substitute g(x) into f(x). So, (f o g)(x) = f(g(x)).
Substituting g(x) = 5x + 7 into f(x) = -6x + 9, we get (-6(5x + 7) + 9).
Simplifying, -30x - 42 + 9 = -30x - 33, which is the composition of the two functions.(f o g)(x) = -30x - 33.
The domain of (f o g)(x) is the same as the domain of g(x), which is all real numbers.
To find (g o f)(x), we substitute f(x) into g(x). So, (g o f)(x) = g(f(x)).
Substituting f(x) = -6x + 9 into g(x) = 5x + 7, we get 5(-6x + 9) + 7.
Simplifying, -30x + 45 + 7 = -30x + 52, which is the composition of the two functions.(g o f)(x) = -30x + 52.
The domain of (g o f)(x) is the same as the domain of f(x), which is all real numbers.