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Math Help - Composite Functions

  1. #1
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    Composite Functions

    Hello all, i need some help with domain and ranges of composite functions.

    1.) f: R --> R, f(x) = X^2 - 4
    g: R+ union {0} ----> R, g(x) = sqrt(x)


    The question was to find f(g(x)) which i found to be x-4. The other part of the question was to find the range which i was completely lost on. Please HELP!

    Thanks in advance.
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    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by andrew2322 View Post
    Hello all, i need some help with domain and ranges of composite functions.

    1.) f: R --> R, f(x) = X^2 - 4
    g: R+ union {0} ----> R, g(x) = sqrt(x)


    The question was to find f(g(x)) which i found to be x-4. The other part of the question was to find the range which i was completely lost on. Please HELP!

    Thanks in advance.
    See the composite you calculated was by this way
     <br /> <br />
{(\sqrt{x})}^2 - 4<br />

    Since the values of x you can use(ie; its domain) is from 0 to infinity

    therfore for those values of x ,the value of your value of function is range

    ie;
    [-4, +infinity}
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  3. #3
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    hello

    hey, i'm not the brightest spark and i have no idea what you mean. Could you be kind enough to explain it one more time?
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    Quote Originally Posted by andrew2322 View Post
    hey, i'm not the brightest spark and i have no idea what you mean. Could you be kind enough to explain it one more time?

    I am sorry for bad explanation

    -See when you found the value of f(g(x)) function what you did was to insert G(x) in place of x

    - So when you did that you must have done this in your mind



    which you further simplified as
    x-4

    - Now what I say is that all values of x which can be put in g(x) are now the domain of f(g(x))

    -Thus only those values of x which are greater than zero can be included
    and thus the domain of f(g(x)) is same as g(x)

    -Now when it comes to the function
    y=x-4
    it can take all the values from -R to +R and y increases as x increases

    - BUT since we have restricted the values of x we will not get all the values

    -So lets put the lowest value of x (zero) to get the minimum
    =0-4 = -4

    - The maximum value of x is infinity and so should be the upper value
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