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Math Help - Finding the Domain

  1. #1
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    Finding the Domain

    Let f(x)=sinx, g(x)=sqrt(1-x^2). Find (fog)(x) and (gof)(x) and their domain.

    Well I can answer (fog)(x) and (gof)(x), which are sin[sqrt(1-x^2)], and [sqrt(1-sinx^2)] respectively. However, I dont know how to find the domain. Any help would be appreciated. Thanks
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by johntuan View Post
    Let f(x)=sinx, g(x)=sqrt(1-x^2). Find (fog)(x) and (gof)(x) and their domain.

    Well I can answer (fog)(x) and (gof)(x), which are sin[sqrt(1-x^2)], and [sqrt(1-sinx^2)] respectively. However, I dont know how to find the domain. Any help would be appreciated. Thanks
    write (\sin x )^2 or \sin^2 x. \sin x^2 = \sin (x^2) is different.

    anyway, the domain is the set of input values (x-values in this case) for which a function is defined. you need to find the x-values that work therefore.

    for the square root function, the thing being square rooted has to be greater than or equal to zero for the function to work. the sine function works for all real values of x

    can you figure out the domains now?
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  3. #3
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    for f o g...would the domain be -1<x<1
    and im not too sure for g o f..because of the sin function
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by johntuan View Post
    for f o g...would the domain be -1<x<1
    yes

    and im not too sure for g o f..because of the sin function
    the same principle applies. you want 1 - \sin^2 x \ge 0. this happens to always be the case, so that the domain is all x \in (- \infty, \infty)
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