Expert: Sherry Wallin - 6/3/2009

Question
QUESTION: Find and simplify the difference of f
f(x-h)-f(x)/h,   h does not equal to zero.
given  f(x)= 1/8x.  Please show me the steps. I am stumpede

ANSWER: Hi June~
    For f(x-h) everywhere there is an x you will put in x-h. that is what you meant by 1/8 x, you meant (1/8)*x right?
and you meant the whole difference divided by h correct?[f(x-h)-f(x)]/h
[(1/8)(x-h)-(1/8)x]/h = [(1/8)x -(1/8)h-(1/8)x]/h = [-(1/8)(h)]/h = -(1/8). Does this show enough of the steps??


Math Prof

---------- FOLLOW-UP ----------

QUESTION: Hi:  It is not (1/8) times X.  It is 1 divived by 8x.  The answer is -1 divided by 8x(x+h).  I don't know how to arrive at that answer.

Answer
Ok. If that is what you meant then what you need to do is use parenthesis like this 1/(8x) otherwise the order of operations says to take 1 divide it by 8 and multiply that result by x written the way you wrote it.
[1/[8*(x-h)]-1/(8x)]/h = [x-(x-h)]/[h*8x(x-h)] = h/[h*8x(x-h)] = 1/(8x(x-h)) which is NOT -1 divided by 8x(x+h), so either the original problem is typed incorrectly or the answer is typed incorrectly. Please check the problem you were given and the answer you were given and make sure they are what you wrote. If the original problem was f(x+h)-f(x)/h, that is x+h and not x-h then you would get the answer you wrote.

Math Prof