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Domain of composite functions

  1. Oct 3, 2009 #1
    1. Find the domain of f(g(x)) where f(x)= radical 25-x^2 and g(x)= ln(x+3)



    2. For the domain of f I got x < or equal to +/- 5 and for the domain of ln(x+3) I got x+3 > 0



    3. (0, 145)

    Thanks for your time. :P
     
  2. jcsd
  3. Oct 3, 2009 #2
    Ol. I suppose you mean -5 <= x <= 5 for the domain of f.

    No.. The first number is wrong. the second number is nearly right, but since this is math and not physics: If you get e^5 in an anwer, just leave it.
     
  4. Oct 3, 2009 #3
    Ah. So, [e^-5, 0)(0, e^5]?
     
    Last edited: Oct 3, 2009
  5. Oct 3, 2009 #4
    Also, how can I find the domain of f o g when f(x) = log(x-1) and g(x)=x/16-x^2?

    For the domain of f(x), I put x>2 (??) and g(x) cannot equal +/- 4. I got this strange answer: (-1+rad65/-2 , -4) (-4, -1-rad65/-2)(-1-rad65/-2 , 4)

    Thank again. :)
     
  6. Oct 3, 2009 #5
    log(x) is defined for x>0. The domain of log(x-1) would be where x-1>0
    You got the domain of g(x) right.

    [tex]f\circ g(x) = f(g(x)) = \log\left(\frac{x}{16-x^2}\right)[/tex]

    Putting the domains together, what will be the domain of the composition? Where will the x values be that make it defined?
     
  7. Oct 4, 2009 #6
    there's no problem at 0. and you forgot about the x+3.
     
  8. Oct 4, 2009 #7
    Alright, for my first problem I've reworked it to (-3, infinity)
     
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