SOLUTION: Hi, I need to find and simplify the difference quotient for f(x + h)- f(x), over h. Where f(x) = 3x + 7. The answer in the book is 3, where h cannot = 0. So I plug in 3x + 7 for

Algebra ->  Functions -> SOLUTION: Hi, I need to find and simplify the difference quotient for f(x + h)- f(x), over h. Where f(x) = 3x + 7. The answer in the book is 3, where h cannot = 0. So I plug in 3x + 7 for      Log On


   

Question 260299: Hi, I need to find and simplify the difference quotient for f(x + h)- f(x), over h. Where f(x) = 3x + 7. The answer in the book is 3, where h cannot = 0. So I plug in 3x + 7 for every f(x), how do I solve this problem and why wouldn't the (3x + 7) and the -(3x + 7) cancel each other out? Thanks for your help, much appreciated.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
First, we have f(x) = 3x + 7.
second, We need to find f(x+h).
f(x+h) = 3(x+h) + 7 = 3x + 3h + 7
--
Now we can find %28f%28x%2Bh%29+-f%28h%29%29%2Fh as
%28f%28x%2Bh%29+-f%28h%29%29%2Fh = %28%283x%2B3h%2B7%29-%283x%2B7%29%29%2Fh
notice what happens in the numerator . . . the 3x + 7 will drop out. This will always happen. We get
%28f%28x%2Bh%29+-f%28h%29%29%2Fh = 3h/h
Now, h approaches 0, so we end with
%28f%28x%2Bh%29+-f%28h%29%29%2Fh = 3.
--