Question

f(x+h)-f(x)Find the difference quotienthwhere h20, for the function below.f(x) = 8x-9Simplify, your answer as much as possible.f(x + h) - f(x)Ü음 .hх5?

Answer 1

Consider the given function,

$f(x)=8x-9$

The difference quotient of a function is given by the formulal,

$DQ=\frac{f(x+h)-f(x)}{h}$

Consider the following,

$\begin{gathered} f(x+h)=8(x+h)-9 \\ f(x+h)=8x+8h-9 \end{gathered}$

Substitute the values in the formula,

$\begin{gathered} DQ=\frac{(8x+8h-9)-(8x-9)}{h} \\ DQ=\frac{8x+8h-9-8x+9}{h} \\ DQ=\frac{8h}{h} \\ DQ=8 \end{gathered}$

Thus, the difference quotient for the given function is 8 units.