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Homework Help: Composite function help! ? - Thanks!

  1. Sep 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Here is the problem:


    2. Relevant equations

    3. The attempt at a solution

    I need help RIGHT from step one.

    Now, step one I would suppose I need to evaluate g(x) ? Which, would be x must be greater than or equal to -5. Correct?

    Then what?
  2. jcsd
  3. Sep 10, 2012 #2
    The first step is to write the function f(g(x)). What this means is that for the function f(x), you substitute x=g(x). Then, you need to find the domain of this f(g(x)) function.
  4. Sep 10, 2012 #3
    Ok, so first thing I would do is write in the g(x) into the f(x) ?

    So, it turns into: f(x) is 3(2-(x + 5)^1/2)^(1/2)

    ? That cant be correct :(
  5. Sep 10, 2012 #4
    Yep, that's correct, except it's f(g(x)), not f(x).
  6. Sep 10, 2012 #5
    Really? lol cool.

    Ok, so then after that, what do I do? This is where I get very confused.
  7. Sep 10, 2012 #6
    Neither square-root can have a negative number inside, so to find the domain, you need to find the intervals of x that make both the inner and outer square-roots positive.

    In other words, x needs to satisfy the conditions:
    [itex]\displaystyle x+5≥0[/itex]
    [itex]\displaystyle 2-\sqrt{x+5}≥0[/itex]
  8. Sep 10, 2012 #7
    So this is all I do to find the formula, as asking in the question. f(x) is 3(2-(x + 5)^1/2)^(1/2)

    x + 5 >= 0 would just be [0, infinity) right? is that what you mean?

    Now sure how you got the 2nd one? what about the 3?
  9. Sep 11, 2012 #8
    The 3 is on the outside of the 2nd square root. You're just trying to make the inside of the square root larger than 0, so the 3 can be disregarded when finding the domain.

    In order to solve the inequalities, you treat it just like any other equation. To solve the first one, you subtract 5 from both sides to get:

    [itex]\displaystyle x+5 ≥ 0[/itex]

    [itex]\displaystyle x ≥ -5[/itex]

    Hopefully that gives you an idea how to solve the second inequality. After you find the solution to both of those, your domain will be the x values that satisfy both inequalities.

    Also, remember that the composite function is not f(x), but f(g(x)). (also written as [itex](f \circ g)(x)[/itex])
    Last edited: Sep 11, 2012
  10. Sep 11, 2012 #9
    I think I got it....

    [-5, -1]

  11. Sep 11, 2012 #10
    Yes, that's right.
  12. Sep 11, 2012 #11
    Yep, I think that's right.
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