Question

For the function ​f(x)=4x+4​,

find ​(a)​ f(x+​h),
​(b)​ f(x+​h)−​f(x), and ​
(c) f(x+h)−f(x) h.

​(a)​ f(x+​h)=?

Answer 1

Explanation:

a)

`f(x+h) = 4(x+h)+4`

`f(x+h)=4x+4h+4`

b)

`f(x+h)-f(x)=4x+4h+4-(4x+4)`

`f(x+h)-f(x)=4x+4h+4-4x-4`

`f(x+h)-f(x)=4h`

c)

`f(x+h)-f(x)h=4x+4h+4-h(4x+4)`

`f(x+h)-f(x)h=4x+4h+4-4hx+4h`

`f(x+h)-f(x)h=-4hx+8h+4x+4`