##### The Algebra of functions

label Algebra
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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

Sep 27th, 2015

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)

Sep 27th, 2015

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?

Sep 27th, 2015

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?

Sep 27th, 2015

Ok I don't have my text with me I will repost when I go home.

Thank you very much for your time

Sep 27th, 2015

OK. I look forward to your repost.

Sep 27th, 2015

it is calculus. I need to find he difference quotient for

f(x) = 1/3x

Sep 27th, 2015

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?

Sep 27th, 2015

yes I do :)

Sep 27th, 2015

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

Sep 27th, 2015

OK.

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.

Sep 27th, 2015

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

Sep 27th, 2015

Denominators in calculus tend to get nasty. :-) Best wishes.

Sep 27th, 2015

Thank You

Sep 27th, 2015

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

Sep 27th, 2015

It is too difficult to do this using text. I'll do it using WORD equations and send you a word file. OK?

Sep 27th, 2015

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.

Sep 27th, 2015

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Sep 27th, 2015
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Sep 27th, 2015
Oct 19th, 2017
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