Q. 75 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 75– 82, find the difference quotient of $f$; that is, find $\frac{f(x+h)- f\left(x\right)}{h}, h\ne 0,$for each function. Be sure to simplify.

$f\left(x\right)=4x+3$

Step-by-Step Solution

Answer

The value of $\frac{f(x+h)- f\left(x\right)}{h}=4$

Step 1. Given Information

In this problems we have to find the difference quotient of $f$; that is, find $\frac{f(x+h)- f\left(x\right)}{h}, h\ne 0,$for given function. Be sure to simplify.

The given function is$f\left(x\right)=4x+3$

Step 2. Firstly we find the value of f ( x + h ) We find the value of f ( x + h ) by putting x = x + h in given function.

$$\begin{gathered} f(x+h)=4(x+h)+3 \\ f(x+h)=4x+4h+3 \end{gathered}$$

Step 3. Putting the value of f ( x )   and   f ( x + h ) in the f ( x + h ) -   f ( x ) h

$$\begin{gathered} \frac{f(x+h)- f\left(x\right)}{h}=\frac{4x+4h+3-(4x+3)}{h} \\ \frac{f(x+h)- f\left(x\right)}{h}=\frac{4x+4h+3-4x-3}{h} \\ \frac{f(x+h)- f\left(x\right)}{h}=\frac{4h}{h} \\ \frac{f(x+h)- f\left(x\right)}{h}=4 \end{gathered}$$