anonymous
  • anonymous
If g(x) = sqrt(x-3) and k(x) = x^2 + 5 then determine (kg)(x).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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rhr12
  • rhr12
(k-g)(5) means plug 5 into both equations, then divide the answer of k(x) by g(x) (g o k)(7) means plug 7 the equation k(x) and then plug the answer you get from k(x) into g(x)
rhr12
  • rhr12
(k - g)(5) =(x²+5)–x–3 = x²-x+2 = 5²-5+2 = 22
anonymous
  • anonymous
\[(kg)(x)=(x^2+5)(\sqrt{x ^{-3})}\]

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rhr12
  • rhr12
hope it helps
anonymous
  • anonymous
Where did you get (k-g) @rhr12? It says to multiply k and g. Were you just giving an example?
anonymous
  • anonymous
I agree with saseal that \[(kg)(x) = k(x)g(x) = (x^2+5)\sqrt{x-3}\]
anonymous
  • anonymous
So what would you plug in for x?
anonymous
  • anonymous
Or would you have to multiply that first?
anonymous
  • anonymous
\[\sqrt{x-3}=(x-3)^{\frac{ 1 }{ 2 }}\]
anonymous
  • anonymous
theres nothing to plug in, theres no value given in the question
anonymous
  • anonymous
So I have to multiply it....Couldn't I just square both equations to get rid of the square root?
anonymous
  • anonymous
i dont think you can multiply, just leave it that way
anonymous
  • anonymous
I don't know think I'd bother multiplying it out, if its actually possible. If I wanted to evaluate (kg) at say x=10, I'd just use it as a normal function and substitute x = 10 everywhere. i.e.\[(kg)(10) = (10^2+5)\sqrt{10-7} = 105\sqrt{7}\]
anonymous
  • anonymous
So just write (x^2 + 5)(sqrt(x - 3))?
anonymous
  • anonymous
yea
anonymous
  • anonymous
It should be \[\sqrt{10-3} \text{ instead of } \sqrt{10-7}\] and yep that is what I'd write
anonymous
  • anonymous
Alright thanks!

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