Question

Let g(x)=9x−10 and evaluate g(x+h)−g(x)/h

Answer 1

`(g(x+h)-g(x))/(h)=9`

Explanation:

we have

`g(x)=9x-10`

To find out g(x+h) substitute the variable x by the variable (x+h) in the function g(x)

so

`g(x+h)=9(x+h)-10`

`g(x+h)=9x+9h-10`

Evaluate

`(g(x+h)-g(x))/(h)`

we have

`g(x+h)=9x+9h-10`

`g(x)=9x-10`

substitute in the expression

`(9x+9h-10-(9x-10))/(h)`

`(9x+9h-10-9x+10))/(h)`

`(9h)/(h)`

`9`

therefore

`(g(x+h)-g(x))/(h)=9`