Answer
$f(-\frac{1}{2})=1$
Work Step by Step
Step 1. Based on the Remainder Theorem, the value of $f(c)$ can be obtained as the remainder of $f(x)$ divided by $x-c$.
Step 2. The coefficients of the dividend $f(x)$ can be identified in order as $\{2,-5,-1,3,2\}$ and the divisor is $x+\frac{1}{2}$; use synthetic division as shown in the figure to get the quotient and the remainder.
Step 3. We can identify the result as $f(x)=(2x^3-6x^2+2x+2)(x+\frac{1}{2})+1$; thus we have $f(-\frac{1}{2})=1$.
