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Math Help - Composition of Function

  1. #1
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    Composition of Function

    Given f(x)= square root (x+4) and g(x)=x^2

    a)g(f(5)) b)f(g(4)) c)g(f(4))
    Please show steps. Thanks.
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  2. #2
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    Quote Originally Posted by johett View Post
    Given f(x)= square root (x+4) and g(x)=x^2

    a)g(f(5)) b)f(g(4)) c)g(f(4))
    Please show steps. Thanks.
    (a) f(5) = 3 \Rightarrow   g(f(5)) = g(3) = 9
    (b) g(4) = 16 \Rightarrow f(g(4)) = \sqrt{20}
    (c) f(4) = \sqrt 8 \Rightarrow g(f(4)) = 8

    OR

    Observe that f(g(x)) = f(x^2) = \sqrt{x^2 + 4}
    and that, g(f(x)) = g(\sqrt{x+4}) = x+4
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