Answer :
Answer:
(a)
[tex]f(x+ h)=8x+8h+3[/tex]
(b)
[tex]f(x+ h)-f(x)=8h[/tex]
(c)
[tex]\dfrac{f(x+ h)-f(x)}{h}=8[/tex]
Step-by-step explanation:
We are given a function f(x) as :
[tex]f(x)=8x+3[/tex]
(a)
[tex]f(x+ h)[/tex]
We will substitute (x+h) in place of x in the function f(x) as follows:
[tex]f(x+h)=8(x+h)+3\\\\i.e.\\\\f(x+h)=8x+8h+3[/tex]
(b)
[tex]f(x+ h)-f(x)[/tex]
Now on subtracting the f(x+h) obtained in part (a) with the function f(x) we have:
[tex]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[/tex]
(c)
[tex]\dfrac{f(x+ h)-f(x)}{h}[/tex]
In this part we will divide the numerator expression which is obtained in part (b) by h to get:
[tex]\dfrac{f(x+ h)-f(x)}{h}=\dfrac{8h}{h}\\\\i.e.\\\\\dfrac{f(x+h)-f(x)}{h}=8[/tex]