Given that `f(x) = 4 x ^2 and g (x) =3-(x)/(2)`, what is the value of `f(g(4))`?

Options

A. 1
B. 4
C. 8
D. 16

Answer

To solve the problem, we need to find the value of \( f(g(4)) \) given the functions \( f(x) = 4x^2 \) and \( g(x) = 3 - \frac{x}{2} \).

### Step-by-Step Solution:

1. **Calculate \( g(4) \)**:
\[ g(x) = 3 - \frac{x}{2} \]
Substitute \( x = 4 \):
\[ g(4) = 3 - \frac{4}{2} \]
Simplifying this:
\[ g(4) = 3 - 2 = 1 \]

2. **Calculate \( f(g(4)) \)**:
We found that \( g(4) = 1 \), so now we need to find \( f(1) \):
\[ f(x) = 4x^2 \]
Substitute \( x = 1 \):
\[ f(1) = 4 \times 1^2 \]
Simplifying this:
\[ f(1) = 4 \times 1 = 4 \]

3. **Final Result**:
Therefore, the value of \( f(g(4)) \) is:
\[ f(g(4)) = f(1) = 4 \]

### Conclusion:
The final answer is \( 4 \).