anonymous
  • anonymous
f(x) = 3x + 2; g(x) = 3x - 5 Find f/g.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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zepdrix
  • zepdrix
\[\large\rm \color{royalblue}{f(x)=3x+2},\qquad \color{orangered}{g(x)=3x-5}\] Then,\[\large\rm \frac{\color{royalblue}{f(x)}}{\color{orangered}{g(x)}}\]just plug in the functions, ya? :)
anonymous
  • anonymous
3x+2/3x-5?
anonymous
  • anonymous
then what would the domain be?

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zepdrix
  • zepdrix
Yes, (3x+2)/(3x-5) The domain is generally going to be all real numbers. But since we have a fraction, we might have a restriction at a location.
zepdrix
  • zepdrix
Recall that in the land of math, we can not divide by 0. \(\large\rm \frac{1}{0}\) <-- This is not a number, this is undefined. This is bad. So what we'll do is, we'll `let` our denominator equal 0 like this. And see if we can find these "bad" values.
zepdrix
  • zepdrix
\[\large\rm 3x-5=0\]This should give us the "bad" value for x.
anonymous
  • anonymous
5/3?
zepdrix
  • zepdrix
Good good good. This is the bad value. Which means our domain consists of every x `except` x=5/3
anonymous
  • anonymous
so would the full answer be (f/g)(x) = Quantity three x plus two divided by three x minus five.; domain {x|x ≠ Five over three. }
anonymous
  • anonymous
Can I ask one more?
zepdrix
  • zepdrix
so would the full answer be (f/g)(x) = Quantity three x plus two divided by `the quantity` three x minus five.; domain {x|x ≠ Five over three. } I would probably add this in, so it's clear that the bottom is an entire quantity, not just a 3x denominator.
zepdrix
  • zepdrix
Sure
anonymous
  • anonymous
f(x) = 7x + 7, g(x) = 6x2 Find (fg)(x).
anonymous
  • anonymous
ok thanks:)
zepdrix
  • zepdrix
\[\large\rm \color{royalblue}{f(x) = 7x + 7},\qquad\qquad \color{orangered}{g(x) = 6x^2}\] \[\large\rm (fg)(x)=\color{royalblue}{f(x)}\color{orangered}{g(x)}\]\[\large\rm =\color{royalblue}{(7x+7)}\color{orangered}{6x^2}\]So here I guess you'll have to do some distributing.
anonymous
  • anonymous
so 42x^3+42x?
anonymous
  • anonymous
?
zepdrix
  • zepdrix
42x^3+42x^2 ya?

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