Missing piece Let g(x) = x² + 3 Find a function ƒ that produces the given composition.


(g o ƒ ) (x) = x²⸍³ + 3

Verified step by step guidance

1. Step 1: Understand the composition (g \circ f)(x) = g(f(x)). We need to find a function f(x) such that when g is applied to f(x), it results in x^{2/3} + 3.
2. Step 2: Recall that g(x) = x^2 + 3. We want g(f(x)) = f(x)^2 + 3 to equal x^{2/3} + 3.
3. Step 3: Set up the equation f(x)^2 + 3 = x^{2/3} + 3.
4. Step 4: Subtract 3 from both sides to isolate the squared term: f(x)^2 = x^{2/3}.
5. Step 5: Solve for f(x) by taking the square root of both sides: f(x) = \sqrt{x^{2/3}}.