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=(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=((8x+8h-9)-(8x-9))/(h) \\ DQ=(8x+8h-9-8x+9)/(h) \\ DQ=(8h)/(h) \\ DQ=8 \end{gathered}`

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