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Math Help - combining functions part 2

  1. #1
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    combining functions part 2

    If:
    f (x) = 3(x+1)^2 (the last 2 means square)
    h(x) = 2/3 (1-x) +3 (the square root is of 1-x only NOT 3) I need to figure out the signs.

    what is (h o f)(x)??

    Thank you very much .
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  2. #2
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    Quote Originally Posted by zdenka View Post
    If:
    f (x) = 3(x+1)^2 (the last 2 means square)
    h(x) = 2/3 (1-x) +3 (the square root is of 1-x only NOT 3) I need to figure out the signs.

    what is (h o f)(x)??

    Thank you very much .
    (hof)(x)=h(f(x))

    f(x)=3(x+1)^2=3x^2+6x+3=t

    \implies (hof)(x)=h(f(x))=h(t)=\frac 23 \sqrt{1-t} +3

    =\frac 23 \sqrt{1-(3x^2+6x+3)}+3=\frac 23 \sqrt{-3x^2-6x-2}+3=\dots
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  3. #3
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    Quote Originally Posted by zdenka View Post
    If:
    f (x) = 3(x+1)^2 (the last 2 means square)
    h(x) = 2/3 (1-x) +3 (the square root is of 1-x only NOT 3) I need to figure out the signs.

    what is (h o f)(x)??

    Thank you very much .
    f(x)=(3x+1)^2

    g(x)=(1-x)^{\frac{2}{3}}+3

    Are these the equations you meant to type?

    If so, plug f(x) in for x in the g(x) equation like so:

    g(x)=(1-f(x))^{\frac{2}{3}}+3

    g(x)=(1-(3x+1)^2)^{\frac{2}{3}}+3
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  4. #4
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    Quote Originally Posted by zdenka View Post
    If:
    f (x) = 3(x+1)^2 (the last 2 means square)
    h(x) = 2/3 (1-x) +3 (the square root is of 1-x only NOT 3) I need to figure out the signs.

    what is (h o f)(x)??

    Thank you very much .
    f(x)=3(x+1)^2

    h(x)=\frac23 \cdot \sqrt{1-x} + 3

    (h\circ f)(x)=h(f(x))

    That means replace the x in h by the term of f:

    h(f(x))= \frac23 \cdot \sqrt{1-3(x+1)^2} + 3

    Try to simplify the last term - but it isn't necessary according to the wording of your question.
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  5. #5
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    Sorry about the wording.... I need to simplify it too....
    Last edited by zdenka; May 19th 2008 at 04:58 PM.
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