If `f(x)=3x-sqrtx and g(x)=x^(2)`, what is `f(g(4))`?

Answer

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

### Step-by-Step Solution:

1. **Calculate \( g(4) \)**:
\[ g(4) = 4^2 = 16 \]

2. **Substitute \( g(4) \) into \( f(x) \)**:
Now we need to find \( f(g(4)) \), which is \( f(16) \).
\[ f(16) = 3(16) - \sqrt{16} \]

3. **Calculate \( f(16) \)**:
- First, calculate \( 3(16) \):
\[ 3(16) = 48 \]
- Next, calculate \( \sqrt{16} \):
\[ \sqrt{16} = 4 \]
- Now substitute these values back into the equation:
\[ f(16) = 48 - 4 = 44 \]

4. **Final Result**:
Therefore, \( f(g(4)) = 44 \).

### Summary:
The value of \( f(g(4)) \) is \( 44 \).