If f(x) = `root(3)(x)` and g(x) = `x^(3) + 8` , find `(f @ g)` (3) .

Options

A. 3.3
B. 5
C. 11
D. 35

Explanation

To solve the problem, we need to find the value of \( (f \circ g)(3) \), where \( f(x) = \sqrt[3]{x} \) and \( g(x) = x^3 + 8 \).

### Step-by-step Solution:

1. **Identify the Functions**:
- We have \( f(x) = \sqrt[3]{x} \) and \( g(x) = x^3 + 8 \).

2. **Find \( g(3) \)**:
- Substitute \( x = 3 \) into \( g(x) \):
\[ g(3) = 3^3 + 8 \]
- Calculate \( 3^3 \):
\[ 3^3 = 27 \]
- Now add 8:
\[ g(3) = 27 + 8 = 35 \]

3. **Find \( f(g(3)) \)**:
- Now we need to find \( f(g(3)) = f(35) \):
\[ f(35) = \sqrt[3]{35} \]

4. **Calculate \( \sqrt[3]{35} \)**:
- The cube root of 35 is approximately:
\[ \sqrt[3]{35} \approx 3.271 \]

5. **Final Answer**:
- Therefore, \( (f \circ g)(3) \approx 3.271 \).

### Summary:
\[ (f \circ g)(3) \approx 3.271 \]