The sections is "The algebra of functions sums, difference products and quotients"
Problem 1 is f(x) = 1/3x
Problem 2 is f(x) = -1/4x
Thank you for the opportunity to help you with your question!
Let f(x) = (1/3) * x and g(x) = (-1/4) * x. If you mean 1/(3x), etc. please advise.
Then f(x) + g(x) = (1/3) * x + (-1/4) * x = ((1/3) -(1/4)] x = [(4-3)/12] x = (1/12)x
Then f(x) - g(x) = (1/3) * x - (-1/4) * x = ((1/3) -(-1/4)] x = [(4+3)/12] x = (7/12)x
Then f(x) * g(x) = (1/3) * x * (-1/4) * x = (1/3)(-1/4)X^2 = (-1/12)x^2
Then f(x) / g(x) = [(1/3) * x] / [(-1/4) * x] = (1/3)/(-1/4) = (-4/3)
They are two separate questions :(. the answer to the first one is -1/3x(x+h). I just don't understand how to get there?
Based on what you have just said, I think you are doing calculus problems. I need to see the full problem statement in order to know how to approach the problem as you initially described it. OK?
Ok I don't have my text with me I will repost when I go home.
Thank you very much for your time
OK. I look forward to your repost.
it is calculus. I need to find he difference quotient for
f(x) = 1/3x
OK. if f(x) = 1/(3x), then f(x+h) = 1/3(x+h) and the DIFFERENCE is then f(x+h) - f(x). The difference QUOTIENT is then [f(x+h) - f(x)] / h = [1/3(x+h) - 1/(3x)] / h. Do you need to simplify this?
yes I do :)
Can you help me to simplify this? I was able to understand up to this point, you are very helpful. I am not sure how to simplify
First, find the LCM of 3(x+h) and 3x. It's 3x(x+h).
Second, multiply the NUMERATOR [1/3(x+h) - 1/(3x)] by 3x(x+h) / 3x(x+h) (which equals 1, right?), getting
x / [3x(x+h)] - (x+h) / [3x(x+h)] = -h /[3x(x+h)].
Then, substituting, [f(x+h) - f(x)] / h = (-h / [3x(x+h)]) / h = -1/[3x(x+h)].
This is as far as I can go. I hope this helps.
That's perfect. this has helped me a great deal. I could do the other problems but not the ones with a denominator whew. I have my first test on Tuesday
Denominators in calculus tend to get nasty. :-) Best wishes.
I'm a bit confused with the third line from the bottom "x / [3x(x+h)] - (x+h) / [3x(x+h)] = -h /[3x(x+h)]"
Im not sure where the x is coming from? im so sorry to bother you again
It is too difficult to do this using text. I'll do it using WORD equations and send you a word file. OK?
Thanks for asking the question. From now on, I'm doing all fractions using WORD.
You should be able to go on from here with my help. Best wishes.
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