Q. 86 - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(x\right)=\frac{2x-B}{3x+4}$ and $f\left(2\right)=\frac{1}{2}$, what is the value of $B$? 

Step-by-Step Solution

Answer

The value of $B=-1$

Step 1. Given Information

If $f\left(x\right)=\frac{2x-B}{3x+4}$ and $f\left(2\right)=\frac{1}{2}$

We have to find the value of $B$.

Step 2. To find the value of B we firstly find the f ( 2 ) by putting x = 2 in the given function.

$$\begin{gathered} f\left(2\right)=\frac{2\times 2-B}{3\times 2+4} \\ f\left(2\right)=\frac{4-B}{6+4} \\ f\left(2\right)=\frac{4-B}{10} \end{gathered}$$

Step 3. Now the function is f ( 2 ) = 4 - B 10 . We know f ( 2 ) = 1 2 so we put the value of f ( 2 ) in the function.

$\frac{1}{2}=\frac{4-B}{10}$

Multiply with 10 on both side

$$\begin{gathered} \frac{1}{2}\times 10=\frac{4-B}{10}\times 10 \\ 5=4-B \end{gathered}$$

Subtract by 4 on both side

$$\begin{gathered} 5-4=4-B-4 \\ 1=-B \end{gathered}$$

Multiply by $-1$ on both side

$$\begin{gathered} 1\times (-1)=-B\times (-1) \\ -1=B \\ B=-1 \end{gathered}$$