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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

1 Answer

1 vote

Answer:

(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

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