Chapter 1 - Functions and Their Graphs - Section 1.1 Functions - 1.1 Assess Your Understanding - Page 55: 86

$B=-1$

It is given, that $f(2)=\frac{1}{2}$. By substituting $x=2$ into the function $f(x)$, we get: $f(2)=\dfrac{2(2)-B}{3(2)+4}$ $\dfrac{1}{2}=\dfrac{4-B}{10}$ Solving this equation for $B$ we get: $\dfrac{4-B}{10}=\dfrac{1}{2}$ $2(4-B)=10(1)$ $8-2B=10\\ 8-2B+2B=10+2B\\ 8=10+2B\\ 8-10=10+2B-10$ $-2=2B$ $-1=B$