Q. 85 - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(x\right)=\frac{3x+8}{2x-A}$ and $f\left(0\right)=2$, what is the value of $A$? 

Step-by-Step Solution

Answer

The value of $A=-4$

Step 1. Given Information

If $f\left(x\right)=\frac{3x+8}{2x-A}$ and $f\left(0\right)=2$

We have to find the value of $A$.

Step 2. To find the value of A we firstly find the f ( 0 ) by putting x = 0 in the given function.

$$\begin{gathered} f\left(0\right)=\frac{3\times 0+8}{2\times 0-A} \\ f\left(0\right)=\frac{8}{-A} \\ f\left(0\right)=-\frac{8}{A} \end{gathered}$$

Step 3. Now the function is f ( 0 ) = - 8 A . We know f ( 0 ) = 2 so we put the value of f ( 0 ) in the function.

$2=-\frac{8}{A}$

Multiply with $A$ on both side

$$\begin{gathered} 2\times A=-\frac{8}{A}\times A \\ 2\times A=-8 \end{gathered}$$

Divide by 2 on both side

$$\begin{gathered} \frac{2}{2}\times A=-\frac{8}{2} \\ A=-4 \end{gathered}$$