Final answer:
c) x⁴. To find the correct substitution for the function f(x), we use the property that x² equals to √x, leading to the answer that √x - 2 / (3 + √x) equals f(x⁴).
Step-by-step explanation:
The question is asking to find the variable substitution for f(x) such that f(?) is equal to the expression √x - 2 / (3 + √x). Using the information provided regarding powers and square roots, we know that x2 is equivalent to √x. Therefore, the expression given can be rewritten with this substitution, resulting in (x2 - 2) / (3 + x2). Matching this to the original function f(x) = x - 2 / (3 + x), we identify the correct substitution is x4 since (x2)2 = x4. Thus, f(x4) = √x - 2 / (3 + √x), making the answer x4.