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

Question

asked Jul 13, 2020 47.8k views

1 Answer

Deestan · Answer 1 · 2020-07-19T23:58:07+0000

(a)

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

(b)

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

(c)

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

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:

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