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Math Help - help!!

  1. #1
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    Question help!!

    i need help on these questions plzz..
    i need to find the domain of fg and f/g:
    f(x)=x+2 g(x)=1/x+2

    f(x)=3x^2+x^4+2 g(x)=4x-3

    nd thanx !!=D
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by lovelygirlXx View Post
    i need help on these questions plzz..
    i need to find the domain of fg and f/g:
    f(x)=x+2 g(x)=1/x+2

    f(x)=3x^2+x^4+2 g(x)=4x-3

    nd thanx !!=D
    the domain is the set of all x-values for which the function is defined. basically, you need to find out what x-values "work" in these formulas.

    example, for f(x) = x + 2 and g(x) = \frac 1{x + 2}

    the domain of f is \text{dom}(f) = (-\infty, \infty), that is, all real numbers. since you can plug in any real number x into x + 2 and it will work, since it is a polynomial

    for g, the domain of g(x) is \text{dom}(g) = (-\infty, -2) \cup (-2, \infty), that is, all real numbers except -2. why not -2? our function does not "work" there, because if x = -2, then we have a fraction in which the denominator is zero. dividing by zero is a no-no (see the pic)

    now, find fg and f/g (do you know how?) and do the same analysis to come up with their domains. note, anything that is not in the domain of f and/or g, will not be in the domain of fg nor f/g


    (i wrote the domains using interval notation. there are several ways you can write them...)
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