Question

Find each of the following for ​

f(x) = 8x + 3. ​
(a) f (x + h)
​(b) f (x + h - f (x) ​
(c) (f (x+h - f(x))/h

Answer 1

(a)

`f(x+ h)=8x+8h+3`

(b)

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

(c)

`(f(x+ h)-f(x))/(h)=8`

Explanation:

We are given a function f(x) as :

`f(x)=8x+3`

(a)

`f(x+ h)`

We will substitute (x+h) in place of x in the function f(x) as follows:

`f(x+h)=8(x+h)+3\\\\i.e.\\\\f(x+h)=8x+8h+3`

(b)

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

Now on subtracting the f(x+h) obtained in part (a) with the function f(x) we have:

`f(x+h)-f(x)=8x+8h+3-(8x+3)\\\\i.e.\\\\f(x+h)-f(x)=8x+8h+3-8x-3\\\\i.e.\\\\f(x+h)-f(x)=8h`

(c)

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

In this part we will divide the numerator expression which is obtained in part (b) by h to get:

`(f(x+ h)-f(x))/(h)=(8h)/(h)\\\\i.e.\\\\(f(x+h)-f(x))/(h)=8`