Question

Find each of the following for ​

Answer 1

Answer:

(a)

          $f(x+ h)=8x+8h+3$  

(b)

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

(c)

             $\dfrac{f(x+ h)-f(x)}{h}=8$

Step-by-step 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)

           $\dfrac{f(x+ h)-f(x)}{h}$            

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

           $\dfrac{f(x+ h)-f(x)}{h}=\dfrac{8h}{h}\\\\i.e.\\\\\dfrac{f(x+h)-f(x)}{h}=8$