Answer
$B=-1$
Work Step by Step
With $f(2)=\frac{1}{2}$, substitute $2$ to $x$ and $\frac{1}{2}$ to $f(2)$ to obtain:
$f(x)=\dfrac{2x-B}{3x+4}$
$f(2)=\dfrac{2(2)-B}{3(2)+4}$
$\dfrac{1}{2}=\dfrac{4-B}{10}$
Cross-multiply to obtain:
$1(10)=2(4-B)$
$10=8-2B$
$10-8=-2B\\
2=-2B\\
\dfrac{2}{-2}=\dfrac{-2B}{-2}\\
-1=B$
