Given that `f(x) = 3x + 7` and `g(x) = (x^2)/(2)`, what is the value of `f(g(4))`?

Options

A. 8
B. 19
C. 31
D. 152

Answer

To find the value of \( f(g(4)) \), we will follow these steps:

### Step 1: Calculate \( g(4) \)
The function \( g(x) \) is given by:
\[ g(x) = \frac{x^2}{2} \]
Substituting \( x = 4 \):
\[ g(4) = \frac{4^2}{2} = \frac{16}{2} = 8 \]

### Step 2: Calculate \( f(g(4)) \) which is \( f(8) \)
The function \( f(x) \) is given by:
\[ f(x) = 3x + 7 \]
Now substituting \( x = 8 \):
\[ f(8) = 3(8) + 7 = 24 + 7 = 31 \]

### Final Answer
Thus, the value of \( f(g(4)) \) is:
\[ \boxed{31} \]