How to solve this?

Question

If f(x) = 3x-5, find f(x+h)—f(x)/h

Answer 1

f ( x + h) =  3 ( x + h) - 5 = 3x + 3h - 5

 

 

f( x + h) - f (x)  = 3x + 3h - 5 - (3x - 5) =

                   

                         3x + 3h - 5 - 3x + 5 =

 

                       3h

 

Finally dividing by h results in 3.

 

Please note that I have ASSUMED you meant the use of

the parenthesis:

 

 [ f( x + h) - f(x) ]/h

 

In contrast, without them, the calculation is TECHNICALLY:

3x + 3h - 5 - (3x - 5)/h

 

in which case the cancellation DOES NOT and WILL NOT occur