Final answer:
The correct options for f(x) and g(x) are f(x) = x and g(x) = 2/x² + 9.
Step-by-step explanation:
The function y = f(g(x)) can be described as the composition of two functions, f(x) and g(x). To determine which options for f(x) and g(x) satisfy the given function, we need to substitute the given options into the composition of f(g(x)).
Let's evaluate each option:
A. f(x) = 2/x² + 9; g(x) = x
B. f(x) = x; g(x) = 2/x² + 9
C. f(x) = 2/x + 9; g(x) = x²
D. f(x) = x²; g(x) = 2/x + 9
By substituting the options into the function, we can see that option B satisfies the given function:
y = f(g(x)) = f(2/x² + 9) = 2/(2/x² + 9) = x²/((2 + 9x²)/x²) = x²/(2/x² + 9/x²) = x²/(2 + 9) = x²/11
Therefore, the correct options for f(x) and g(x) are f(x) = x and g(x) = 2/x² + 9.