Answer: f(x) = √x and g(x) = 4x + 8.
Explanation:
The given problem asks us to determine which pair of functions, f and g, could correctly represent the composite function (f • g)(x) = h(x), where h(x) is equal to the square root of the quantity 4 times x plus 8 end quantity.
Let's analyze each option and see if it fits the criteria:
1. f(x) = √(2x + 4) and g(x) = √(2x + 4):
To determine if this option is correct, we need to find (f • g)(x) and check if it matches h(x).
We have (f • g)(x) = f(g(x)) = f(√(2x + 4)).
Substituting f(x) = √(2x + 4) into the expression, we get f(√(2x + 4)) = √(2(√(2x + 4)) + 4).
Simplifying further, we get √(4x + 8 + 4) = √(4x + 12).
However, h(x) = √(4x + 8).
Thus, this option does not accurately represent (f • g)(x) = h(x).
2. f(x) = 4x + 8 and g(x) = √x:
Following the same steps as above, we find (f • g)(x) = f(g(x)) = f(√x) = 4√x + 8.
However, h(x) = √(4x + 8).
Therefore, this option does not correctly represent (f • g)(x) = h(x).
3. f(x) = √x and g(x) = 4x + 8:
Using the same process, we have (f • g)(x) = f(g(x)) = f(4x + 8) = √(4x + 8).
This matches h(x) = √(4x + 8), so this option accurately represents (f • g)(x) = h(x).
4. f(x) = √(2x + 4) and g(x) = √2:
Similarly, we find (f • g)(x) = f(g(x)) = f(√2) = √(2√2 + 4).
However, h(x) = √(4x + 8).
Thus, this option does not correctly represent (f • g)(x) = h(x).
After analyzing all the options, the only pair of functions that accurately represents the composite function (f • g)(x) = h(x) is:
f(x) = √x and g(x) = 4x + 8.
Hope this helps.