SOLUTION: Find f (a), f (a + h), and the difference quotient for the function given below, where h does not equal 0. f(x) = x/(x + 5)

Algebra ->  Functions -> SOLUTION: Find f (a), f (a + h), and the difference quotient for the function given below, where h does not equal 0. f(x) = x/(x + 5)      Log On


   

Question 1144668: Find f (a), f (a + h), and the difference quotient for the function given below, where h does not equal 0. f(x) = x/(x + 5)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
 

f%28x%29+=+x%2F%28x+%2B+5%29
f%28a%29+=+a%2F%28a+%2B+5%29
f%28a%2Bh%29+=+%28a%2Bh%29%2F%28%28a%2Bh%29+%2B+5%29=%28a%2Bh%29%2F%28a%2Bh%2B5%29
f%28a%2Bh%29-f%28a%29=%28a%2Bh%29%2F%28a%2Bh%2B5%29-a%2F%28a+%2B+5%29



Everything in the top cancels except terms that contain h,
and some of them may cancel.

f%28a%2Bh%29-f%28a%29=%285h%29%2F%28%28a%2B5%29%28a%2Bh%2B5%29%29

Now we form the difference quotient by dividing by h on the
left, and doing the equivalent multiplication by 1/h on the
right. [Dividing by h and multiplying by 1/h are the same.]



The h's cancel on the right and we are left with



Edwin