Question

For the function: f(x) = 6x, find and simplifya. f(x) = f(a)/ x-a=b. f(x+h)-f(x)/ h =

Answer 1

The Solution:

Given:

Required:

Simplify the following:

`(a)\text{ }(f(x)-f(a))/(x-a)=(6x-6a)/(x-a)=(6(x-a))/(x-a)=6`
`(b)\text{ }(f(x+h)-f(x))/(h)`

Where:

`f(x+h)=6(x+h)=6x+6h`

Substitute:

`\text{ }(f(x+h)-f(x))/(h)=(6x+6h-6x)/(h)=(6h)/(h)=6`

Answers:

(a) 6

(b) 6