SOLUTION: In College Algebra we begin to work with and simplify the difference quotient, which is given by the formula f(x+h)-f(x). Find the difference quotient for the following function

Algebra ->  Rational-functions -> SOLUTION: In College Algebra we begin to work with and simplify the difference quotient, which is given by the formula f(x+h)-f(x). Find the difference quotient for the following function       Log On


   

Question 1006175: In College Algebra we begin to work with and simplify the difference quotient, which is given by the formula f(x+h)-f(x). Find the difference quotient for the following function by completing the following steps:

(x)=5x-4

1. Find f(x + h) = __________________________



2. Find f(x) = ____________________________



3. Find f(x+h) – f(x) = ______________________



4. Find = ______________________

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming the given function is f(x) = 5x-4

================================================
1)

f(x) = 5x-4
f(x+h) = 5(x+h)-4 ... replace every x with x+h
f(x+h) = 5x+5h-4

================================================
2)

f(x) = 5x-4

================================================
3)

f(x+h) = 5x+5h-4
f(x) = 5x-4
f(x+h)-f(x) = (5x+5h-4) - (5x-4)
f(x+h)-f(x) = 5x+5h-4 - 5x+4
f(x+h)-f(x) = (5x-5x)+5h+(-4+4)
f(x+h)-f(x) = (0x)+5h+(0)
f(x+h)-f(x) = (0)+5h+(0)
f(x+h)-f(x) = 5h

================================================
4)
This part is blank, but I'm going to assume you meant to write %28f%28x%2Bh%29-f%28x%29%29%2Fh


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

%28f%28x%2Bh%29-f%28x%29%29%2Fh=%285h%29%2Fh

%28f%28x%2Bh%29-f%28x%29%29%2Fh=5


So in the end, %28f%28x%2Bh%29-f%28x%29%29%2Fh=5 when f%28x%29=5x-4