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

Answer

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

### Step-by-Step Solution:

1. **Calculate \( f(4) \)**:
- We start by substituting \( x = 4 \) into the function \( f(x) \).
\[ f(4) = 3(4) - \sqrt{4} \]
- Calculate \( 3(4) \):
\[ 3(4) = 12 \]
- Calculate \( \sqrt{4} \):
\[ \sqrt{4} = 2 \]
- Now, substitute these values back into the equation:
\[ f(4) = 12 - 2 = 10 \]

2. **Calculate \( g(f(4)) \)**:
- Now that we have \( f(4) = 10 \), we need to find \( g(10) \).
- Substitute \( x = 10 \) into the function \( g(x) \):
\[ g(10) = 10^2 \]
- Calculate \( 10^2 \):
\[ 10^2 = 100 \]

3. **Final Result**:
- Therefore, the value of \( g(f(4)) \) is:
\[ g(f(4)) = 100 \]

### Summary:
The final answer is \( g(f(4)) = 100 \).