If `f(x)=(x^(2))/(2)-(x^(2))/(2)+x-16`, find `f((1)/(2))`

Answer

To find \( f\left(\frac{1}{2}\right) \) for the function \( f(x) = \frac{x^2}{2} - \frac{x^2}{2} + x - 16 \), we can follow these steps:

### Step 1: Simplify the function
First, let's simplify the function \( f(x) \):
\[ f(x) = \frac{x^2}{2} - \frac{x^2}{2} + x - 16 \]
Notice that \( \frac{x^2}{2} - \frac{x^2}{2} = 0 \). Therefore, we can simplify \( f(x) \) to:
\[ f(x) = x - 16 \]

### Step 2: Substitute \( x = \frac{1}{2} \)
Now, we need to find \( f\left(\frac{1}{2}\right) \):
\[ f\left(\frac{1}{2}\right) = \frac{1}{2} - 16 \]

### Step 3: Perform the arithmetic
Next, we perform the subtraction:
\[ f\left(\frac{1}{2}\right) = \frac{1}{2} - 16 = \frac{1}{2} - \frac{32}{2} = \frac{1 - 32}{2} = \frac{-31}{2} \]

### Final Answer
Thus, the value of \( f\left(\frac{1}{2}\right) \) is:
\[ f\left(\frac{1}{2}\right) = -\frac{31}{2} \]

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