1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Composite function help! ? - Thanks!

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

    Here is the problem:

    2wntl60.png


    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]
    and
    [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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Composite function help! ? - Thanks!
  1. Composite functions (Replies: 21)

  2. Composition functions (Replies: 14)

Loading...