Answer is: option4

\( \frac{1}{2} a - \frac{5}{2} \)

Solution:

We are given:

\[ f(x) = \frac{x}{2} - 3 \]

Evaluating at \( x = a \):

\[ f(a) = \frac{a}{2} - 3 \]

The derivative is:

\[ f'(x) = \frac{1}{2} \]

Evaluating at \( x = a \):

\[ f'(a) = \frac{1}{2} \]

Now, computing \( f(a) + f'(a) \):

\[ f(a) + f'(a) = \frac{a}{2} - 3 + \frac{1}{2} \]

\[ = \frac{a}{2} - \frac{5}{2} \]

Answer: \[ \frac{a}{2} - \frac{5}{2} \]