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{ }\frac{f(x)-f(a)}{x-a}=\frac{6x-6a}{x-a}=\frac{6(x-a)}{x-a}=6$$(b)\text{ }\frac{f(x+h)-f(x)}{h}$

Where:

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

Substitute:

$\text{ }\frac{f(x+h)-f(x)}{h}=\frac{6x+6h-6x}{h}=\frac{6h}{h}=6$

Answers:

(a) 6

(b) 6